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References

Published online by Cambridge University Press:  28 February 2020

Marcelo Aguiar  and
Swapneel Mahajan
Marcelo Aguiar
Affiliation:
Cornell University, Ithaca
Swapneel Mahajan
Affiliation:
Indian Institute of Technology, Mumbai
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Bimonoids for Hyperplane Arrangements , pp. 763 - 801
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Print publication year: 2020

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References

1. Abe, E., Hopf algebras, Cambridge Tracts in Mathematics, vol. 74, Cambridge University Press, Cambridge-New York, 1980, Translated from the Japanese by Hisae Kinoshita and Hiroko Tanaka. 128, 129, 232, 233, 332, 383, 526, 714Google Scholar
2. Abramenko, P. and Brown, K. S., Buildings, Graduate Texts in Mathematics, vol. 248, Springer, New York, 2008, Theory and applications. 72CrossRefGoogle Scholar
3. Adámek, J., Theory of mathematical structures, D. Reidel Publishing Co., Dordrecht, 1983. 131Google Scholar
4. Adámek, J., Herrlich, H., Strecker, G. E., Abstract and concrete categories: the joy of cats, Repr. Theory Appl. Categ. (2006), no. 17, 1–507, Reprint of the 1990 original. 760Google Scholar
5. Adámek, J., Rosický, J., Vitale, E. M., Algebraic theories, Cambridge Tracts in Mathematics, vol. 184, Cambridge University Press, Cambridge, 2011, A categorical introduction to general algebra, With a foreword by F. W. Lawvere. 760Google Scholar
6. Adams, J. F., Infinite loop spaces, Annals of Mathematics Studies, vol. 90, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1978. 203Google Scholar
7. Agore, A.-L., Categorical constructions for Hopf algebras, Comm. Algebra 39 (2011), no. 4, 1476 – 1481. 282Google Scholar
8. Agrawala, V. K., Invariants of generalized Lie algebras, Hadronic J. 4 (1980/81), no. 2, 444–496. 673Google Scholar
9. Aguiar, M., André, C., Benedetti, C., Bergeron, N., Chen, Z., Diaconis, P., Hendrickson, A., Hsiao, S., Isaacs, I. M., Jedwab, A., Johnson, K., Karaali, G., Lauve, A., Le, T., Lewis, S., Li, H., Magaard, K., Marberg, E., Novelli, J.-C., Pang, C. Y. A., Saliola, F. V., Tevlin, L., Thibon, J.-Y., Thiem, N., Venkateswaran, V., Vinroot, C. R., Yan, N., Zabrocki, M., Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras, Adv. Math. 229 (2012), no. 4, 2310 – 2337. 333Google Scholar
10. Aguiar, M. and Ardila, F., Hopf monoids and generalized permutahedra, available at arXiv:1709.07504. 132, 332, 527Google Scholar
11. Aguiar, M., Bergeron, N., Sottile, F., Combinatorial Hopf algebras and generalized Dehn-Sommerville relations, Compos. Math. 142 (2006), no. 1, 1–30. 333, 526Google Scholar
12. Aguiar, M., Bergeron, N., Thiem, N., Hopf monoids from class functions on unitriangular matrices, Algebra Number Theory 7 (2013), no. 7, 1743–1779. 132, 333Google Scholar
13. Aguiar, M. and Ferrer Santos, W., Galois connections for incidence Hopf algebras of partially ordered sets, Adv. Math. 151 (2000), no. 1, 71–100. 527Google Scholar
14. Aguiar, M., Haim, M., López Franco, I., Monads on higher monoidal categories, Appl. Categ. Structures 26 (2018), no. 3, 413–458. 736Google Scholar
15. Aguiar, M. and Lauve, A., Lagrange’s theorem for Hopf monoids in species, Canad. J. Math. 65 (2013), no. 2, 241–265. 132Google Scholar
16. Aguiar, M. and Lauve, A., The characteristic polynomial of the Adams operators on graded connected Hopf algebras, Algebra Number Theory 9 (2015), no. 3, 547–583. 232, 234, 468, 526, 527Google Scholar
17. Aguiar, M. and Mahajan, S., Coxeter groups and Hopf algebras, Fields Institute Monographs, vol. 23, American Mathematical Society, Providence, RI, 2006, With a foreword by Nantel Bergeron. xi, xiii, xvi, 71, 72, 129, 132, 233, 281, 282, 315, 330, 333, 525, 526, 527, 636, 637Google Scholar
18. Aguiar, M. and Mahajan, S., Monoidal functors, species and Hopf algebras, CRM Monograph Series, vol. 29, American Mathematical Society, Providence, RI, 2010, With forewords by Kenneth Brown and Stephen Chase and André Joyal. xi, xii, xiii, xiv, xvi, xix, 71, 124, 127, 129, 130, 131, 132, 133, 158, 168, 179, 180, 203, 204, 234, 277, 279, 280, 281, 282, 315, 330, 331, 332, 333, 334, 335, 358, 381, 383, 525, 526, 527, 528, 574, 636, 676, 708, 716, 723, 724, 736, 737, 751, 760, 762Google Scholar
19. M.Aguiar, and S. Mahajan, , Hopf monoids in the category of species, Hopf algebras and tensor categories, Contemp. Math., vol. 585, Amer. Math. Soc., Providence, RI, 2013, pp. 17–124. xi, xii, xiii, xvi, 124, 127, 132, 234, 282, 332, 440, 441, 468, 527, 573, 676, 715Google Scholar
20. Aguiar, M. and Mahajan, S., On the Hadamard product of Hopf monoids, Canad. J. Math. 66 (2014), no. 3, 481–504. 383, 574, 636Google Scholar
21. Aguiar, M. and Mahajan, S., Topics in hyperplane arrangements, Mathematical Surveys and Monographs, vol. 226, American Mathematical Society, Providence, RI, 2017. xi, xiii, xiv, xix, xx, 19, 20, 23, 24, 27, 28, 29, 32, 33, 36, 37, 38, 39, 44, 47, 48, 49, 52, 55, 57, 66, 67, 69, 70, 71, 72, 167, 199, 200, 204, 278, 281, 298, 320, 330, 331, 334, 356, 358, 425, 426, 429, 439, 440, 441, 468, 478, 493, 509, 519, 524, 525, 528, 554, 559, 572, 573, 574, 607, 608, 617, 633, 635, 636, 637, 677, 708, 709, 712, 713, 715, 716Google Scholar
22. Aguiar, M. and Sottile, F., Cocommutative Hopf algebras of permutations and trees, J. Algebraic Combin. 22 (2005), 451–470. 234, 279Google Scholar
23. Aguiar, M. and Sottile, F., Structure of the Malvenuto-Reutenauer Hopf algebra of permutations, Adv. Math. 191 (2005), no. 2, 225–275. 526, 636Google Scholar
24. Aguiar, M. and Sottile, F., Structure of the Loday-Ronco Hopf algebra of trees, J. Algebra 295 (2006), no. 2, 473–511. 527Google Scholar
25. Aguilar, M., Gitler, S., Prieto, C., Algebraic topology from a homotopical viewpoint, Universitext, Springer-Verlag, New York, 2002, Translated from the Spanish by Stephen Bruce Sontz. 133Google Scholar
26. Aissaoui, S. and Makhlouf, A., On classification of finite-dimensional superbialgebras and Hopf superalgebras, SIGMA Symmetry Integrability Geom. Methods Appl. 10 (2014), Paper 001, 24. 130Google Scholar
27. Amelunxen, D. and Lotz, M., Intrinsic volumes of polyhedral cones: a combinatorial perspective, Discrete Comput. Geom. 58 (2017), no. 2, 371–409. 72Google Scholar
28. André, M., L’algèbre de Lie d’un anneau local, Symposia Mathematica, Vol. IV (IN-DAM, Rome, 1968/69), Academic Press, London, 1970, pp. 337–375. 675Google Scholar
29. André, M., Hopf algebras with divided powers, J. Algebra 18 (1971), 19–50. 278, 675, 676, 715Google Scholar
30. André, M., Hopf and Eilenberg-MacLane algebras, Reports of the Midwest Category Seminar, V (Zürich, 1970), Lecture Notes in Mathematics, Vol. 195, Springer, Berlin, 1971, pp. 1–28. 573, 715Google Scholar
31. Andrews, S., The Hopf monoid on nonnesting supercharacters of pattern groups, J. Algebraic Combin. 42 (2015), no. 1, 129–164. 132Google Scholar
32. Andruskiewitsch, N., About finite dimensional Hopf algebras, Quantum symmetries in theoretical physics and mathematics (Bariloche, 2000), Contemp. Math., vol. 294, Amer. Math. Soc., Providence, RI, 2002, pp. 1–57. 715Google Scholar
33. Andruskiewitsch, N., Angiono, I., Bagio, D., Examples of pointed color Hopf algebras, J. Algebra Appl. 13 (2014), no. 2, 1350098, 28. 130Google Scholar
34. Andruskiewitsch, N., Angiono, I., Yamane, H., On pointed Hopf superalgebras, New developments in Lie theory and its applications, Contemp. Math., vol. 544, Amer. Math. Soc., Providence, RI, 2011, pp. 123–140. 130CrossRefGoogle Scholar
35. Andruskiewitsch, N. and Ferrer Santos, W., The beginnings of the theory of Hopf algebras, Acta Appl. Math. 108 (2009), no. 1, 3–17. 129Google Scholar
36. Anel, M. and Joyal, A., Sweedler theory for (co)algebras and the bar-cobar constructions, available at arXiv:1309.6952. 281, 382, 441Google Scholar
37. Anquela, J. A. and Cortés, T., Cofree coalgebras, Comm. Algebra 24 (1996), no. 1, 357–371. 281Google Scholar
38. Anquela, J. A., Cortés, T., Montaner, F., Nonassociative coalgebras, Comm. Algebra 22 (1994), no. 12, 4693–4716. 675Google Scholar
39. Araki, S., Differential Hopf algebras and the cohomology mod 3 of the compact exceptional groups E7 and E8, Ann. of Math. (2) 73 (1961), 404–436. 128, 572Google Scholar
40. Arbib, M. A. and Manes, E. G., Arrows, structures, and functors, Academic Press, New York-London, 1975, The categorical imperative. 131, 760Google Scholar
41. Ardila, F., Algebraic and geometric methods in enumerative combinatorics, Handbook of enumerative combinatorics, Discrete Math. Appl., CRC Press, Boca Raton, FL, 2015, pp. 3–172. 72Google Scholar
42. Ardizzoni, A., The Heyneman-Radford theorem for monoidal categories, J. Algebra 308 (2007), no. 1, 63–72. 233Google Scholar
43. Ardizzoni, A., A Milnor-Moore type theorem for primitively generated braided bialgebras, J. Algebra 327 (2011), 337–365. 677, 716Google Scholar
44. Ardizzoni, A.,On primitively generated braided bialgebras, Algebr. Represent. Theory 15 (2012), no. 4, 639–673. 677, 716Google Scholar
45. Ardizzoni, A.,Universal enveloping algebras of PBW type, Glasg. Math. J. 54 (2012), no. 1, 9–26. 716Google Scholar
46. Ardizzoni, A. and Menini, C., Milnor-Moore categories and monadic decomposition, J. Algebra 448 (2016), 488–563. 131, 677, 716Google Scholar
47. Ardizzoni, A., Menini, C., Ştefan, D., Braided bialgebras of Hecke-type, J. Algebra 321 (2009), no. 3, 847–865. 716Google Scholar
48. Arkowitz, M., Introduction to homotopy theory, Universitext, Springer, New York, 2011. 133Google Scholar
49. Artamonov, V. A., The structure of Hopf algebras, Algebra. Topology. Geometry, Vol. 29 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1991, Translated in J. Math. Sci. 71 (1994), no. 2, 2289–2328, pp. 3–63. 129Google Scholar
50. Artamonov, V. A., Coalgebras, Hopf algebras, The concise handbook of algebra (A. V. Mikhalev and G. F. Pilz, eds.), Kluwer Academic Publishers, Dordrecht, 2002, pp. 305–311. 129Google Scholar
51. Aubry, M., Twisted Lie algebras and idempotent of Dynkin, Sém. Lothar. Combin. 62 (2009/10), Art. B62b, 22. 676Google Scholar
52. Aubry, M., Hall basis of twisted Lie algebras, J. Algebraic Combin. 32 (2010), no. 2, 267–286. 676Google Scholar
53. Auslander, M., Reiten, I., Smalø, S. O., Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics, vol. 36, Cambridge University Press, Cambridge, 1997, Corrected reprint of the 1995 original. 204Google Scholar
54. Awodey, S., Category theory, second ed., Oxford Logic Guides, vol. 52, Oxford University Press, Oxford, 2010. xiv, 737, 760Google Scholar
55. Bachmann, H., The algebra of bi-brackets and regularized multiple Eisenstein series, J. Number Theory 200 (2019), 260–294. 608Google Scholar
56. Baez, J. C., Hochschild homology in a braided tensor category, Trans. Amer. Math. Soc. 344 (1994), no. 2, 885–906. 131Google Scholar
57. Baez, J. C. and Dolan, J., Higher-dimensional algebra and topological quantum field theory, J. Math. Phys. 36 (1995), no. 11, 6073–6105. 133Google Scholar
58. Baez, J. C. and Dolan, J., From finite sets to Feynman diagrams, Mathematics unlimited—2001 and beyond, Springer, Berlin, 2001, pp. 29–50. 132Google Scholar
59. Baez, J. C. and Shulman, M., Lectures on n-categories and cohomology, Towards higher categories, IMA Vol. Math. Appl., vol. 152, Springer, New York, 2010, pp. 1–68. 132Google Scholar
60. Baez, J. C. and Stay, M. A., Physics, topology, logic and computation: a Rosetta Stone, New structures for physics, Lecture Notes in Phys., vol. 813, Springer, Heidelberg, 2011, pp. 95–172. 737Google Scholar
61. Bahturin, Y. A., Identical relations in Lie algebras, VNU Science Press, b.v., Utrecht, 1987, Translated from the Russian by Bahturin. 674, 713Google Scholar
62. Bahturin, Y. A., Basic structures of modern algebra, Mathematics and its Applications, vol. 265, Kluwer Academic Publishers Group, Dordrecht, 1993. 713Google Scholar
63. Bahturin, Y. A., Fischman, D., Montgomery, S., On the generalized Lie structure of associative algebras, Israel J. Math. 96 (1996), no. part A, 27–48. 676Google Scholar
64. Bahturin, Y. A., Mikhalev, A. A., Petrogradsky, V. M., Zaicev, M. V., Infinite-dimensional Lie superalgebras, De Gruyter Expositions in Mathematics, vol. 7, Walter de Gruyter & Co., Berlin, 1992. 130, 673, 674, 675, 714Google Scholar
65. Bahturin, Y. A., Mikhalev, A. A., Zaicev, M. V., Infinite-dimensional Lie superalgebras, Handbook of algebra, Vol. 2, Elsevier/North-Holland, Amsterdam, 2000, pp. 579–614. 714Google Scholar
66. Baker, A. and Richter, B., Quasisymmetric functions from a topological point of view, Math. Scand. 103 (2008), no. 2, 208–242. 333Google Scholar
67. Baker-Jarvis, D., Bergeron, N., Thiem, N., The antipode and primitive elements in the Hopf monoid of supercharacters, J. Algebraic Combin. 40 (2014), no. 4, 903–938. 132, 527Google Scholar
68. Balteanu, C. and Fiedorowicz, Z., The coherence theorem for 2-fold monoidal categories, An. Univ. Timişoara Ser. Mat.-Inform. 34 (1996), no. 1, 29–48. 736Google Scholar
69. Balteanu, C., Fiedorowicz, Z., Schwänzl, R., Vogt, R. M., Iterated monoidal categories, Adv. Math. 176 (2003), no. 2, 277–349. 133, 736Google Scholar
70. Barr, M., Composite cotriples and derived functors, Sem. on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Springer, Berlin, 1969, pp. 336–356. 760Google Scholar
71. Barr, M., Coalgebras over a commutative ring, J. Algebra 32 (1974), no. 3, 600–610. 281, 382Google Scholar
72. Barr, M., Composite cotriples and derived functors, Repr. Theory Appl. Categ. (2008), no. 18, 249–266, Sem. on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Reprint of the 1969 original, With a preface to the reprint by Michael Barr. 760Google Scholar
73. Barr, M. and Wells, C., Toposes, triples and theories, Repr. Theory Appl. Categ. (2005), no. 12, x+288, Corrected reprint of the 1985 original. 760, 761Google Scholar
74. Barratt, M. G., Twisted Lie algebras, Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, Lecture Notes in Math., vol. 658, Springer, Berlin, 1978, pp. 9–15. 132, 282, 331, 676Google Scholar
75. Bartocci, C., Bruzzo, U., Hernández Ruipérez, D., The geometry of supermanifolds, Mathematics and its Applications, vol. 71, Kluwer Academic Publishers Group, Dordrecht, 1991. 130Google Scholar
76. Batanin, M. A., The Eckmann-Hilton argument and higher operads, Adv. Math. 217 (2008), no. 1, 334–385. 133Google Scholar
77. Batanin, M. A. and Markl, M., Operadic categories and duoidal Deligne’s conjecture, Adv. Math. 285 (2015), 1630–1687. 736Google Scholar
78. Batchelor, M., Measuring coalgebras, quantum group-like objects and noncommutative geometry, Differential geometric methods in theoretical physics (Rapallo, 1990), Lecture Notes in Phys., vol. 375, Springer, Berlin, 1991, pp. 47–60. 382Google Scholar
79. Batchelor, M., Difference operators, measuring coalgebras, and quantum group-like objects, Adv. Math. 105 (1994), no. 2, 190–218. 382Google Scholar
80. Batchelor, M., Measuring comodules—their applications, J. Geom. Phys. 36 (2000), no. 3-4, 251–269. 382Google Scholar
81. Baudoin, F., An introduction to the geometry of stochastic flows, Imperial College Press, London, 2004. 712Google Scholar
82. Baudoin, F., The tangent space to a hypoelliptic diffusion and applications, Séminaire de Probabilités XXXVIII, Lecture Notes in Math., vol. 1857, Springer, Berlin, 2005, pp. 338–362. 712Google Scholar
83. Beck, J. M., Triples, algebras and cohomology, Ph.D. thesis, Columbia University, 1967. 760Google Scholar
84. Beck, J. M., Distributive laws, Sem. on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Springer, Berlin, 1969, pp. 119–140. 760Google Scholar
85. Beck, J. M., On H-spaces and infinite loop spaces, Category Theory, Homology Theory and their Applications, III (Battelle Institute Conference, Seattle, Wash., 1968, Vol. Three), Springer, Berlin, 1969, pp. 139–153. 737Google Scholar
86. Beck, J. M.,Triples, algebras and cohomology, Repr. Theory Appl. Categ. (2003), no. 2, 1–59. 760Google Scholar
87. Beck, J. M., Distributive laws, Repr. Theory Appl. Categ. (2008), no. 18, 95–112, Sem. on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Reprint of the 1969 original, With a preface to the reprint by Michael Barr. 760Google Scholar
88. Beilinson, A., Ginzburg, V., Schechtman, V. V., Koszul duality, J. Geom. Phys. 5 (1988), no. 3, 317–350. 204Google Scholar
89. Bénabou, J., Catégories avec multiplication, C. R. Acad. Sci. Paris 256 (1963), 1887– 1890. 735Google Scholar
90. Bénabou, J., Algèbre élémentaire dans les catégories avec multiplication, C. R. Acad. Sci. Paris 258 (1964), 771–774. 130, 735Google Scholar
91. Bénabou, J., Catégories relatives, C. R. Acad. Sci. Paris 260 (1965), 3824–3827. 736Google Scholar
92. Bénabou, J., Introduction to bicategories, Reports of the Midwest Category Seminar, Springer, Berlin, 1967, pp. 1–77. 131, 736, 760Google Scholar
93. Bénabou, J., Structures algébriques dans les catégories, Cahiers Topologie Géom. Différentielle 10 (1968), 1–126. 131Google Scholar
94. Benedetti, C. and Bergeron, N., The antipode of linearized Hopf monoids, Sém. Lothar. Combin. 78B (2017), Art. 13, 12. 132, 527Google Scholar
95. Benedetti, C., Hallam, J., Machacek, J., Combinatorial Hopf algebras of simplicial complexes, SIAM J. Discrete Math. 30 (2016), no. 3, 1737–1757. 527Google Scholar
96. Benedetti, C. and Sagan, B. E., Antipodes and involutions, J. Combin. Theory Ser. A 148 (2017), 275–315. 527Google Scholar
97. Benson, D. B., The shuffle bialgebra, Mathematical foundations of programming language semantics (New Orleans, LA, 1987), Lecture Notes in Comput. Sci., vol. 298, Springer, Berlin, 1988, pp. 616–637. 278Google Scholar
98. Benson, D. B., Bialgebras: some foundations for distributed and concurrent computation, Fund. Inform. 12 (1989), no. 4, 427–486. 131, 278, 279Google Scholar
99. Berezin, F. A., Introduction to superanalysis, Mathematical Physics and Applied Mathematics, vol. 9, D. Reidel Publishing Co., Dordrecht, 1987, Edited and with a foreword by A. A. Kirillov, With an appendix by V. I. Ogievetsky, Translated from the Russian by J. Niederle and R. Kotecký, Translation edited by Dimitri Leĭtes. 714Google Scholar
100. Berezin, F. A. and Kac, G. I., Lie groups with commuting and anticommuting parameters, Mat. Sb. (N.S.) 82 (124) (1970), 343–359. 673Google Scholar
101. Berger, C. and Moerdijk, I., Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003), no. 4, 805–831. 203Google Scholar
102. Bergeron, F., Labelle, G., Leroux, P., Combinatorial species and tree-like structures, Cambridge University Press, Cambridge, 1998, Translated from the 1994 French original by Margaret Readdy, With a foreword by Gian-Carlo Rota. 131, 132, 203, 331, 381, 383Google Scholar
103. Bergeron, F. and Lauve, A., Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables, Electron. J. Combin. 17 (2010), no. 1, Research Paper 166, 17. 333Google Scholar
104. Bergeron, N. and Ceballos, C., A Hopf algebra of subword complexes, Adv. Math. 305 (2017), 1163–1201. 527Google Scholar
105. Bergeron, N., Hohlweg, C., Rosas, M. H., Zabrocki, M., Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables, Electron. J. Combin. 13 (2006), no. 1, Research Paper 75, 19. 333Google Scholar
106. Bergeron, N. and Zabrocki, M., The Hopf algebras of symmetric functions and quasi-symmetric functions in non-commutative variables are free and co-free, J. Algebra Appl. 8 (2009), no. 4, 581–600. 333Google Scholar
107. Bergman, G. M., Everybody knows what a Hopf algebra is, Group actions on rings (Brunswick, Maine, 1984), Contemp. Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985, pp. 25–48. 129Google Scholar
108. Berstein, I., On co-groups in the category of graded algebras, Trans. Amer. Math. Soc. 115 (1965), 257–269. 574Google Scholar
109. Bertet, K., Krob, D., Morvan, M., Novelli, J.-C., Phan, T. H. D., Thibon, J.-Y., An overview of Λ-type operations on quasi-symmetric functions, Comm. Algebra 29 (2001), no. 9, 4277–4303, Special issue dedicated to Alexei Ivanovich Kostrikin. 333Google Scholar
110. Bhaskaracharya, Siddhantashiromani, 1150. 71Google Scholar
111. Bialynicki-Birula, I., Mielnik, B., Plebański, J., Explicit solution of the continuous Baker-Campbell-Hausdorff problem and a new expression for the phase operator, Annals of Physics 51 (1969), no. 1, 187–200. 440, 712Google Scholar
112. Bidigare, T. P., Hyperplane arrangement face algebras and their associated Markov chains, Ph.D. thesis, University of Michigan, 1997. 71Google Scholar
113. Bidigare, T. P., Hanlon, P., Rockmore, D., A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements, Duke Math. J. 99 (1999), no. 1, 135–174. 71Google Scholar
114. Birkhoff, G., Representability of Lie algebras and Lie groups by matrices, Ann. of Math. (2) 38 (1937), no. 2, 526–532. 671, 673, 674, 711Google Scholar
115. Birkhoff, G. and Whitman, P. M., Representation of Jordan and Lie algebras, Trans. Amer. Math. Soc. 65 (1949), 116–136. 711Google Scholar
116. Björner, A. and Brenti, F., Combinatorics of Coxeter groups, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005. 72Google Scholar
117. Björner, A., Las Vergnas, M., Sturmfels, B., White, N., Ziegler, G. M., Oriented matroids, Encyclopedia of Mathematics and its Applications, vol. 46, Cambridge University Press, Cambridge, 1993. 72Google Scholar
118. Blanchard, A. A., Structure species and constructive functors, Canadian J. Math. 26 (1974), 1217–1227. 131Google Scholar
119. Bland, R. G., Complementary orthogonal subspaces of Rn and orientability of matroids, Ph.D. thesis, Cornell University, 1974. 71Google Scholar
120. Blessenohl, D. and Schocker, M., Noncommutative character theory of the symmetric group, Imperial College Press, London, 2005. 332, 636Google Scholar
121. Block, R. E., Commutative Hopf algebras, Lie coalgebras, and divided powers, J. Algebra 96 (1985), no. 1, 275–306. 278, 675, 676, 715Google Scholar
122. Block, R. E., Determination of the irreducible divided power Hopf algebras, J. Algebra 96 (1985), no. 1, 307–317. 572, 715Google Scholar
123. Block, R. E. and Griffing, G., Recognizable formal series on trees and cofree coalgebraic systems, J. Algebra 215 (1999), no. 2, 543–573. 281Google Scholar
124. Block, R. E. and Leroux, P., Generalized dual coalgebras of algebras, with applications to cofree coalgebras, J. Pure Appl. Algebra 36 (1985), no. 1, 15–21. 281Google Scholar
125. Blute, R. F. and Scott, P. J., The shuffle Hopf algebra and noncommutative full completeness, J. Symbolic Logic 63 (1998), no. 4, 1413–1436. 278Google Scholar
126. Boardman, J. M. and Vogt, R. M., Homotopy invariant algebraic structures on topological spaces, Springer-Verlag, Berlin, 1973, Lecture Notes in Mathematics, Vol. 347. 203, 760Google Scholar
127. Böhm, G., Hopf algebras and their generalizations from a category theoretical point of view, Lecture Notes in Mathematics, vol. 2226, Springer, Cham, 2018. 736, 761Google Scholar
128. Böhm, G., Chen, Y., Zhang, L., On Hopf monoids in duoidal categories, J. Algebra 394 (2013), 139–172. 736Google Scholar
129. Böhm, G., Gómez-Torrecillas, J., López-Centella, E., On the category of weak bialgebras, J. Algebra 399 (2014), 801–844. 736Google Scholar
130. Bonfiglioli, A. and Fulci, R., Topics in noncommutative algebra, Lecture Notes in Mathematics, vol. 2034, Springer, Heidelberg, 2012, The theorem of Campbell, Baker, Hausdorff and Dynkin. 129, 279, 440, 674, 713Google Scholar
131. Booker, T. and Street, R., Tannaka duality and convolution for duoidal categories, Theory Appl. Categ. 28 (2013), No. 6, 166–205. 736Google Scholar
132. Borceux, F., Handbook of categorical algebra. 1, Encyclopedia of Mathematics and its Applications, vol. 50, Cambridge University Press, Cambridge, 1994. 493, 494, 760Google Scholar
133. Borceux, F., Handbook of categorical algebra. 2, Encyclopedia of Mathematics and its Applications, vol. 51, Cambridge University Press, Cambridge, 1994. 736, 737, 761Google Scholar
134. Borceux, F. and Dejean, D., Cauchy completion in category theory, Cahiers Topologie Géom. Différentielle Catég. 27 (1986), no. 2, 133–146. 494Google Scholar
135. Borel, A., Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115–207. 127, 232, 572, 573Google Scholar
136. Borel, A., Sur l’homologie et la cohomologie des groupes de Lie compacts connexes, Amer. J. Math. 76 (1954), 273–342. 232, 233, 572, 573Google Scholar
137. Borel, A., Topology of Lie groups and characteristic classes, Bull. Amer. Math. Soc. 61 (1955), 397–432. 232, 573Google Scholar
138. Borel, A., Essays in the history of Lie groups and algebraic groups, History of Mathematics, vol. 21, American Mathematical Society, Providence, RI; London Mathematical Society, Cambridge, 2001. 671Google Scholar
139. Borovik, A. V. and Borovik, A., Mirrors and reflections, Universitext, Springer, New York, 2010, The geometry of finite reflection groups. 72Google Scholar
140. Borovik, A. V., Gelfand, I. M., White, N., Coxeter matroids, Progress in Mathematics, vol. 216, Birkhäuser Boston, Inc., Boston, MA, 2003. 72Google Scholar
141. Boseck, H., Graded Lie algebras, graded Hopf algebras, and graded algebraic groups, Convergence structures and applications, II (Schwerin, 1983), Abh. Akad. Wiss. DDR, Abt. Math. Naturwiss. Tech., vol. 84, Akademie-Verlag, Berlin, 1984, pp. 15–24. 713Google Scholar
142. Boseck, H., On the enveloping algebra of a Lie superalgebra and its dual and bidual, Proceedings of the second international conference on operator algebras, ideals, and their applications in theoretical physics (Leipzig, 1983), Teubner-Texte Math., vol. 67, Teubner, Leipzig, 1984, pp. 57–63. 130, 713Google Scholar
143. Boseck, H., Affine Lie supergroups, Math. Nachr. 143 (1989), 303–327. 130Google Scholar
144. Bouc, S., Biset functors for finite groups, Lecture Notes in Mathematics, vol. 1990, Springer-Verlag, Berlin, 2010. 133Google Scholar
145. Bourbaki, N., Éléments de mathématique. 22. Première partie: Les structures fon-damentales de l’analyse. Livre 1: Théorie des ensembles. Chapitre 4: Structures, Actualités Sci. Ind. no. 1258, Hermann, Paris, 1957. 131Google Scholar
146. Bourbaki, N., Éléments de mathématique. XXVI. Groupes et algèbres de Lie. Chapitre 1: Algèbres de Lie, Actualités Sci. Ind. No. 1285. Hermann, Paris, 1960. 712Google Scholar
147. Bourbaki, N., Elements of mathematics. Theory of sets, Translated from the French, Hermann, Publishers in Arts and Science, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. 131Google Scholar
148. Bourbaki, N., Éléments de mathématique, Masson, Paris, 1981, Groupes et algèbres de Lie. Chapitres 4, 5 et 6. 72Google Scholar
149. Bourbaki, N., Algebra I. Chapters 1–3, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1998, Translated from the French, Reprint of the 1989 English translation. 128, 278, 279, 381, 525Google Scholar
150. Bourbaki, N., Lie groups and Lie algebras. Chapters 1–3, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1998, Translated from the French, Reprint of the 1989 English translation. 440, 671, 674, 675, 714Google Scholar
151. Bourgin, D. G., Modern algebraic topology, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. 232, 233, 572Google Scholar
152. Bradley, D. M., Multiple q-zeta values, J. Algebra 283 (2005), no. 2, 752–798. 333Google Scholar
153. Braverman, A. and Gaitsgory, D., Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type, J. Algebra 181 (1996), no. 2, 315–328. 716Google Scholar
154. Bredon, G. E., Topology and geometry, Graduate Texts in Mathematics, vol. 139, Springer-Verlag, New York, 1997, Corrected third printing of the 1993 original. 133Google Scholar
155. Breen, L., Une lettre à P. Deligne au sujet des 2-catégories tressées, 1988, available at https://www.math.univ-paris13.fr/~breen/. 736Google Scholar
156. Bremner, M. R. and Dotsenko, V., Algebraic operads, CRC Press, Boca Raton, FL, 2016, An algorithmic companion. 132, 203, 332, 383, 713Google Scholar
157. Bridson, M. R. and Haefliger, A., Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften, vol. 319, Springer-Verlag, Berlin, 1999. 204Google Scholar
158. Bröcker, T. and Dieck, T. tom, Representations of compact Lie groups, Graduate Texts in Mathematics, vol. 98, Springer-Verlag, New York, 1985. 525Google Scholar
159. Brouder, C. and Schmitt, W. R., Renormalization as a functor on bialgebras, J. Pure Appl. Algebra 209 (2007), no. 2, 477–495. 280Google Scholar
160. Browder, W., On differential Hopf algebras, Trans. Amer. Math. Soc. 107 (1963), 153–176. 128, 232, 233, 234, 573Google Scholar
161. Brown, K. A. and Goodearl, K. R., Lectures on algebraic quantum groups, Advanced Courses in Mathematics. CRM Barcelona, Birkhäuser Verlag, Basel, 2002. 129, 383Google Scholar
162. Brown, K. S., Semigroups, rings, and Markov chains, J. Theoret. Probab. 13 (2000), no. 3, 871–938. 71Google Scholar
163. Brown, K. S., Semigroup and ring theoretical methods in probability, Representations of finite dimensional algebras and related topics in Lie theory and geometry, Fields Inst. Commun., vol. 40, Amer. Math. Soc., Providence, RI, 2004, pp. 3–26. 71Google Scholar
164. Brown, K. S. and Diaconis, P., Random walks and hyperplane arrangements, Ann. Probab. 26 (1998), no. 4, 1813–1854. 71Google Scholar
165. Brown, R., Higgins, P. J., Sivera, R., Nonabelian algebraic topology, EMS Tracts in Mathematics, vol. 15, European Mathematical Society (EMS), Zürich, 2011, Filtered spaces, crossed complexes, cubical homotopy groupoids. 133, 737Google Scholar
166. Bruguières, A., Lack, S., Virelizier, A., Hopf monads on monoidal categories, Adv. Math. 227 (2011), no. 2, 745–800. 737, 761Google Scholar
167. Bruguières, A. and Virelizier, A., Hopf monads, Adv. Math. 215 (2007), no. 2, 679–733. 761Google Scholar
168. Bruned, Y., Curry, C., Ebrahimi-Fard, K., Quasi-shuffle algebras and renormalisation of rough differential equations, available at arXiv:1801.02964. 608Google Scholar
169. Brzeziński, T. and Hajac, P. M., Coalgebra extensions and algebra coextensions of Galois type, Comm. Algebra 27 (1999), no. 3, 1347–1367. 761Google Scholar
170. Brzeziński, T. and Majid, S., Coalgebra bundles, Comm. Math. Phys. 191 (1998), no. 2, 467–492. 761Google Scholar
171. Brzeziński, T. and Wisbauer, R., Corings and comodules, London Mathematical Society Lecture Note Series, vol. 309, Cambridge University Press, Cambridge, 2003. 279, 381, 526Google Scholar
172. Buchstaber, V. M. and Panov, T. E., Toric topology, Mathematical Surveys and Monographs, vol. 204, American Mathematical Society, Providence, RI, 2015. 574, 715Google Scholar
173. Bucur, I. and Deleanu, A., Introduction to the theory of categories and functors, With the collaboration of Peter J. Hilton and Nicolae Popescu. Pure and Applied Mathematics, Vol. XIX, Interscience Publication John Wiley & Sons, Ltd., London-New York-Sydney, 1968. 131Google Scholar
174. Bui, V. C., Duchamp, G. H. E., Minh, H. N., Ngô, Q. H., Tollu, C., (Pure) transcendence bases in φ-deformed shuffle bialgebras, Sém. Lothar. Combin. 74 ([2015-2018]), Art. B74f, 22. 280, 440, 608, 676, 713Google Scholar
175. Bulacu, D., Caenepeel, S., Panaite, F., Van Oystaeyen, F., Quasi-Hopf algebras, Encyclopedia of Mathematics and its Applications, vol. 171, Cambridge University Press, Cambridge, 2019, A categorical approach. 129, 131, 526, 736Google Scholar
176. Bunge, M. C., Relative functor categories and categories of algebras, J. Algebra 11 (1969), 64–101. 736, 737Google Scholar
177. Burroni, E., Algèbres non déterministiques et D-catégories, Cahiers Topologie Géom. Différentielle 14 (1973), no. 4, 417–475, 480–481, Conférences du Colloque sur l’Algèbre des Catégories (Amiens, 1973), I. 760, 761Google Scholar
178. Burroni, E., Algèbres relatives à une loi distributive, C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A443–A446. 760Google Scholar
179. Burroni, E., Catégories relatives à une loi distributive, C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A669–A672. 760Google Scholar
180. Burroni, E., Lois distributives mixtes, C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A897– A900. 760, 761Google Scholar
181. Caenepeel, S., Brauer groups, Hopf algebras and Galois theory, K-Monographs in Mathematics, vol. 4, Kluwer Academic Publishers, Dordrecht, 1998. 381, 526Google Scholar
182. Caenepeel, S., Militaru, G., Zhu, S., Frobenius and separable functors for generalized module categories and nonlinear equations, Lecture Notes in Mathematics, vol. 1787, Springer-Verlag, Berlin, 2002. 381, 526Google Scholar
183. Campbell, A., Skew-enriched categories, Appl. Categ. Structures 26 (2018), no. 3, 597–615. 737Google Scholar
184. Capelli, A., Sur les Opérations dans la théorie des formes algébriques, Math. Ann. 37 (1890), no. 1, 1–37. 711Google Scholar
185. Carboni, A. and Street, R., Order ideals in categories, Pacific J. Math. 124 (1986), no. 2, 275–288. 494Google Scholar
186. Carmeli, C., Caston, L., Fioresi, R., Mathematical foundations of supersymmetry, EMS Series of Lectures in Mathematics, European Mathematical Society (EMS), Zürich, 2011. 130, 714Google Scholar
187. Cartan, E., La topologie des espaces représentatifs des groupes de Lie, Enseignement Math. 35 (1936), 177–200. 571Google Scholar
188. Cartan, H., Séminaire Henri Cartan de l’Ecole Normale Supérieure, 1954/1955. Algèbres d’Eilenberg-MacLane et homotopie, Secrétariat mathématique, 11 rue Pierre Curie, Paris, 1956, 2ème éd. 278, 279Google Scholar
189. Cartan, H. and Eilenberg, S., Homological algebra, Princeton University Press, Princeton, N. J., 1956. 127, 128, 525, 674, 675, 712, 713Google Scholar
190. Cartier, P., Le théorème de Poincaré-Birkhoff-Witt, Séminaire Sophus Lie; Volume 1. Exposé no. 1, Secrétariat mathématique, Paris, 1954–1955, pp. 1–10. 712Google Scholar
191. Cartier, P., Effacement dans la cohomologie des algèbres de Lie, Séminaire N. Bourbaki; Volume 3. Exposé no. 116, 1954–1956, pp. 161–167. 672Google Scholar
192. Cartier, P., Hyperalgèbres et groupes de Lie formels, Séminaire Sophus Lie; Volume 2, Secrétariat mathématique, Paris, 1955–56. 127, 128, 232, 233, 279, 671, 673, 674, 712, 714Google Scholar
193. Cartier, P., Dualité de Tannaka des groupes et des algèbres de Lie, C. R. Acad. Sci. Paris 242 (1956), 322–325. 128, 676Google Scholar
194. Cartier, P., Théorie différentielle des groupes algébriques, C. R. Acad. Sci. Paris 244 (1957), 540–542. 128, 232, 714Google Scholar
195. Cartier, P., Remarques sur le théorème de Birkhoff-Witt, Ann. Scuola Norm. Sup. Pisa (3) 12 (1958), 1–4. 712Google Scholar
196. Cartier, P., Groupes algébriques et groupes formels, Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962), Librairie Universitaire, Louvain; GauthierVillars, Paris, 1962, pp. 87–111. 232, 573, 714, 715Google Scholar
197. Cartier, P., Groupes formels associés aux anneaux de Witt généralisés, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), A49–A52. 333Google Scholar
198. Cartier, P., On the structure of free Baxter algebras, Advances in Math. 9 (1972), 253– 265. 280Google Scholar
199. Cartier, P., Les arrangements d’hyperplans: un chapitre de géométrie combinatoire, Bourbaki Seminar, Vol. 1980/81, Lecture Notes in Math., vol. 901, Springer, Berlin-New York, 1981, pp. 1–22. 72Google Scholar
200. Cartier, P., An introduction to quantum groups, Algebraic groups and their generalizations: quantum and infinite-dimensional methods (University Park, PA, 1991), Proc. Sympos. Pure Math., vol. 56, Amer. Math. Soc., Providence, RI, 1994, pp. 19–42. 128, 714Google Scholar
201. Cartier, P., Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents, Astérisque (2002), no. 282, Exp. No. 885, viii, 137–173, Séminaire Bourbaki, Vol. 2000/2001. 333Google Scholar
202. Cartier, P., A primer of Hopf algebras, Frontiers in number theory, physics, and geometry. II, Springer, Berlin, 2007, pp. 537–615. 129, 233, 234, 440, 468, 525, 572, 573, 714, 715Google Scholar
203. Cartier, P. and Foata, D. C., Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Mathematics, No. 85, Springer-Verlag, Berlin-New York, 1969. 133Google Scholar
204. Ceyhan, O. and Marcolli, M., Algebraic renormalization and Feynman integrals in configuration spaces, Adv. Theor. Math. Phys. 18 (2014), no. 2, 469–511. 440Google Scholar
205. Chari, V. and Pressley, A., A guide to quantum groups, Cambridge University Press, Cambridge, 1995, Corrected reprint of the 1994 original. 129, 383Google Scholar
206. Chase, S. U. and Sweedler, M. E., Hopf algebras and Galois theory, Lecture Notes in Mathematics, Vol. 97, Springer-Verlag, Berlin-New York, 1969. 525Google Scholar
207. Chen, K.-t., Algebraic paths, J. Algebra 10 (1968), 8–36. 278Google Scholar
208. Chen, K.-t., Fox, R. H., Lyndon, R. C., Free differential calculus. IV. The quotient groups of the lower central series, Ann. of Math. (2) 68 (1958), 81–95. 278Google Scholar
209. Cheng, S.-J. and Wang, W., Dualities and representations of Lie superalgebras, Graduate Studies in Mathematics, vol. 144, American Mathematical Society, Providence, RI, 2012. 714Google Scholar
210. Chevalley, C., Theory of Lie Groups. I, Princeton Mathematical Series, vol. 8, Princeton University Press, Princeton, N. J., 1946. 671Google Scholar
211. Chevalley, C., The construction and study of certain important algebras, The Mathematical Society of Japan, Tokyo, 1955. 130Google Scholar
212. Chevalley, C., Théorie des groupes de Lie. Tome III. Théorèmes généraux sur les algèbres de Lie, Actualités Sci. Ind. no. 1226, Hermann & Cie, Paris, 1955. 713Google Scholar
213. Chevalley, C., Fundamental concepts of algebra, Academic Press Inc., New York, 1956. 130Google Scholar
214. Chevalley, C. and Eilenberg, S., Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85–124. 572Google Scholar
215. Chmutov, S. V., Duzhin, S. V., Mostovoy, J., Introduction to Vassiliev knot invariants, Cambridge University Press, Cambridge, 2012. 439, 573, 713Google Scholar
216. Cohen, P. B., Eyre, T. M. W., Hudson, R. L., Higher order Itô product formula and generators of evolutions and flows, Proceedings of the International Quantum Structures Association, Quantum Structures’94 (Prague, 1994), vol. 34, 1995, pp. 1481–1486. 281Google Scholar
217. Cohn, P. M., Sur le critère de Friedrichs pour les commutateurs dans une algèbre associative libre, C. R. Acad. Sci. Paris 239 (1954), 743–745. 674Google Scholar
218. Cohn, P. M., A remark on the Birkhoff-Witt theorem, J. London Math. Soc. 38 (1963), 197–203. 712Google Scholar
219. Cohn, P. M., Universal algebra, second ed., Mathematics and its Applications, vol. 6, D. Reidel Publishing Co., Dordrecht-Boston, Mass., 1981. 712Google Scholar
220. Connes, A. and Kreimer, D., Hopf algebras, renormalization and noncommutative geometry, Comm. Math. Phys. 199 (1998), no. 1, 203–242. 527Google Scholar
221. Connes, A. and Marcolli, M., Noncommutative geometry, quantum fields and motives, American Mathematical Society Colloquium Publications, vol. 55, American Mathematical Society, Providence, RI; Hindustan Book Agency, New Delhi, 2008. 128, 278, 494, 714Google Scholar
222. Corry, L., Modern algebra and the rise of mathematical structures, second ed., Birkhäuser Verlag, Basel, 2004. 131Google Scholar
223. Corwin, L. J., Ne’eman, Y., Sternberg, S., Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry), Rev. Modern Phys. 47 (1975), 573–603. 713Google Scholar
224. Costa, A. and Steinberg, B., The Schützenberger category of a semigroup, Semigroup Forum 91 (2015), no. 3, 543–559. 494Google Scholar
225. Crole, R. L., Categories for types, Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 1993. 737Google Scholar
226. Curry, C., Ebrahimi-Fard, K., Malham, S. J. A., Wiese, A., Lévy processes and quasi-shuffle algebras, Stochastics 86 (2014), no. 4, 632–642. 281Google Scholar
227. Curry, C., Ebrahimi-Fard, K., Malham, S. J. A., Wiese, A., Algebraic structures and stochastic differential equations driven by Lévy processes, Proc. A. 475 (2019), no. 2221, 20180567, 27. 281, 526Google Scholar
228. Dăscălescu, S., Năstăsescu, C., Raianu, Ş., Hopf algebras, Monographs and Textbooks in Pure and Applied Mathematics, vol. 235, Marcel Dekker, Inc., New York, 2001, An introduction. 129, 233, 279, 281, 381, 526Google Scholar
229. Davis, M. W., The geometry and topology of Coxeter groups, London Mathematical Society Monographs Series, vol. 32, Princeton University Press, Princeton, NJ, 2008. 72Google Scholar
230. Day, B. J., Construction of biclosed categories, Ph.D. thesis, University of New South Wales, 1970. 737Google Scholar
231. Day, B. J., On closed categories of functors, Reports of the Midwest Category Seminar, IV, Lecture Notes in Mathematics, Vol. 137, Springer, Berlin, 1970, pp. 1–38. 737Google Scholar
232. Day, B. J., On closed categories of functors. II, Category Seminar (Proc. Sem., Sydney, 1972/1973), 1974, pp. 20–54. Lecture Notes in Math., Vol. 420. 737Google Scholar
233. Day, B. J., Middle-four maps and net categories, available at arXiv:0911.5200. 736Google Scholar
234. Day, B. J. and Kelly, G. M., Enriched functor categories, Reports of the Midwest Category Seminar, III, Springer, Berlin, 1969, pp. 178–191. 737Google Scholar
235. De Concini, C. and Procesi, C., Quantum groups, D-modules, representation theory, and quantum groups (Venice, 1992), Lecture Notes in Math., vol. 1565, Springer, Berlin, 1993, pp. 31–140. 129Google Scholar
236. De Concini, C. and Procesi, C., Topics in hyperplane arrangements, polytopes and box-splines, Universitext, Springer, New York, 2011. 72Google Scholar
237. de Graaf, W. A., Lie algebras: theory and algorithms, North-Holland Mathematical Library, vol. 56, North-Holland Publishing Co., Amsterdam, 2000. 713Google Scholar
238. Deligne, P. and Milne, J. S., Tannakian categories, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Mathematics, vol. 900, Springer-Verlag, Berlin-New York, 1982, pp. 101–228. 737Google Scholar
239. Deligne, P. and Morgan, J. W., Notes on supersymmetry (following Joseph Bernstein), Quantum fields and strings: a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997), Amer. Math. Soc., Providence, RI, 1999, pp. 41–97. 130, 676, 714, 716Google Scholar
240. Delucchi, E. and Pagaria, R., The homotopy type of elliptic arrangements, available at arXiv:1911.02905. 204Google Scholar
241. Demazure, M., Lectures on p-divisible groups, Lecture Notes in Mathematics, Vol. 302, Springer-Verlag, Berlin-New York, 1972. 525, 574, 714Google Scholar
242. Demazure, M. and Gabriel, P., Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs, Masson & Cie, Éditeur, Paris; North-Holland Publishing Co., Amsterdam, 1970. 128, 440, 525, 572, 574, 715Google Scholar
243. Demazure, M. and Gabriel, P., Introduction to algebraic geometry and algebraic groups, North-Holland Mathematics Studies, vol. 39, North-Holland Publishing Co., Amsterdam-New York, 1980, Translated from the French by J. Bell. 128, 440, 525Google Scholar
244. Deng, B., Du, J., Parshall, B., Wang, J., Finite dimensional algebras and quantum groups, Mathematical Surveys and Monographs, vol. 150, American Mathematical Society, Providence, RI, 2008. 129, 381, 713Google Scholar
245. Diaconescu, R., Change of base for some toposes, Ph.D. thesis, Dalhousie University (Canada), 1973. 761Google Scholar
246. Diaconescu, R., Change of base for toposes with generators, J. Pure Appl. Algebra 6 (1975), no. 3, 191–218. 761Google Scholar
247. Diaconis, P., Pang, C. Y. A., Ram, A., Hopf algebras and Markov chains: two examples and a theory, J. Algebraic Combin. 39 (2014), no. 3, 527–585. 468Google Scholar
248. Dieudonné, J., Groupes de Lie et hyperalgébres de Lie sur un corps de caractéristique p > 0, Comment. Math. Helv. 28 (1954), 87–118. 128+0,+Comment.+Math.+Helv.+28+(1954),+87–118.+128>Google Scholar
249. Dieudonné, J., Groupes de Lie et hyperalgèbres de Lie sur un corps de caractéristique p > 0. V, Bull. Soc. Math. France 84 (1956), 207–239. 128+0.+V,+Bull.+Soc.+Math.+France+84+(1956),+207–239.+128>Google Scholar
250. Dieudonné, J., Introduction to the theory of formal groups, Marcel Dekker, Inc., New York, 1973, Pure and Applied Mathematics, 20. 128, 232, 525, 573, 715Google Scholar
251. Dieudonné, J., A history of algebraic and differential topology 1900–1960, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2009, Reprint of the 1989 edition. 572, 573Google Scholar
252. Dimca, A., Hyperplane arrangements, Universitext, Springer, Cham, 2017, An introduction. 72Google Scholar
253. Ditters, E. J., Curves and exponential series in the theory of noncommutative formal groups, Ph.D. thesis, University of Nijmegen, 1969. 333, 525, 607Google Scholar
254. Ditters, E. J., Sur une série exponentielle non commutative définie sur les corps de caractéristique p, C. R. Acad. Sci. Paris Sér. A-B 268 (1969), A580–A582. 333, 525Google Scholar
255. Ditters, E. J., Curves and formal (co)groups, Invent. Math. 17 (1972), 1–20. 333, 525, 607Google Scholar
256. Ditters, E. J., Groupes formels, U. E. R. Mathématique, Université de Paris XI, Orsay, 1975, Cours de 3e cycle 1973–1974, Publications Mathématiques d’Orsay, No. 149 75.42. 333, 714Google Scholar
257. Ditters, E. J. and Scholtens, A. C. J., Free polynomial generators for the Hopf algebra QSym of quasisymmetric functions, J. Pure Appl. Algebra 144 (1999), no. 3, 213–227. 333, 439Google Scholar
258. Dixmier, J., Enveloping algebras, Graduate Studies in Mathematics, vol. 11, American Mathematical Society, Providence, RI, 1996, Revised reprint of the 1977 translation. 676, 712, 713Google Scholar
259. Dobrev, V. K., Invariant differential operators. Vol. 3. Supersymmetry, De Gruyter Studies in Mathematical Physics, vol. 49, De Gruyter, Berlin, 2018. 714Google Scholar
260. Dold, A., Lectures on algebraic topology, Classics in Mathematics, Springer-Verlag, Berlin, 1995, Reprint of the 1972 edition. 572Google Scholar
261. Dowling, T. A. and Wilson, R. M., Whitney number inequalities for geometric lattices, Proc. Amer. Math. Soc. 47 (1975), 504–512. 334Google Scholar
262. Drinfeld, V. G., Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, RI, 1987, pp. 798–820. 129, 675Google Scholar
263. Drinfeld, V. G., Quasi-Hopf algebras, Algebra i Analiz 1 (1989), no. 6, 114–148. 468Google Scholar
264. Dubuc, E. J., Adjoint triangles, Reports of the Midwest Category Seminar, II, Springer, Berlin, 1968, pp. 69–91. 761Google Scholar
265. Dubuc, E. J., Kan extensions in enriched category theory, Lecture Notes in Mathematics, Vol. 145, Springer-Verlag, Berlin-New York, 1970. 736, 737Google Scholar
266. Duchamp, G. H. E., Enjalbert, J.-Y., Minh, H. N., Tollu, C., The mechanics of shuffle products and their siblings, Discrete Math. 340 (2017), no. 9, 2286–2300. 281, 676Google Scholar
267. Duchamp, G. H. E., Hivert, F., Novelli, J.-C., Thibon, J.-Y., Noncommutative symmetric functions VII: free quasi-symmetric functions revisited, Ann. Comb. 15 (2011), no. 4, 655–673. 636Google Scholar
268. Duchamp, G. H. E., Hivert, F., Thibon, J.-Y., Noncommutative symmetric functions. VI. Free quasi-symmetric functions and related algebras, Internat. J. Algebra Comput. 12 (2002), no. 5, 671–717. 333, 636Google Scholar
269. Duchamp, G. H. E., Klyachko, A., Krob, D., Thibon, J.-Y., Noncommutative symmetric functions. III. Deformations of Cauchy and convolution algebras, Discrete Math. Theor. Comput. Sci. 1 (1997), no. 1, 159–216, Lie computations (Marseille, 1994). 279, 333Google Scholar
270. Duchamp, G. H. E. and Krob, D., Free partially commutative structures, J. Algebra 156 (1993), no. 2, 318–361. 133Google Scholar
271. Ebrahimi-Fard, K., Gracia-Bondía, J. M., Patras, F., A Lie theoretic approach to renormalization, Comm. Math. Phys. 276 (2007), no. 2, 519–549. 440Google Scholar
272. Ebrahimi-Fard, K. and Guo, L., Mixable shuffles, quasi-shuffles and Hopf algebras, J. Algebraic Combin. 24 (2006), no. 1, 83–101. 280Google Scholar
273. Ebrahimi-Fard, K., Malham, S. J. A., Patras, F., Wiese, A., The exponential Lie series for continuous semimartingales, Proc. A. 471 (2015), no. 2184, 20150429, 19. 281, 608, 712, 713Google Scholar
274. Ebrahimi-Fard, K., Malham, S. J. A., Patras, F., Wiese, A., Flows and stochastic Taylor series in Itô calculus, J. Phys. A 48 (2015), no. 49, 495202, 17. 281, 712, 713Google Scholar
275. Ebrahimi-Fard, K., Manchon, D., Patras, F., A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov’s recursion, J. Noncommut. Geom. 3 (2009), no. 2, 181–222. 440Google Scholar
276. Eckmann, B. and Hilton, P. J., Group-like structures in general categories. I. Multiplications and comultiplications, Math. Ann. 145 (1961/1962), 227–255. 131, 132Google Scholar
277. Ehrenborg, R., On posets and Hopf algebras, Adv. Math. 119 (1996), no. 1, 1–25. 333, 525, 526Google Scholar
278. Ehresmann, C., Gattungen von lokalen Strukturen, Jber. Deutsch. Math.-Verein. 60 (1957), 49–77. 131Google Scholar
279. Ehresmann, C., Élargissements de catégories, Séminaire Ehresmann. Topologie et géométrie différentielle 3 (1960-1962). 131Google Scholar
280. Ehresmann, C., Catégories doubles et catégories structurées, C. R. Acad. Sci. Paris 256 (1963), 1198–1201. 760Google Scholar
281. Ehresmann, C., Catégories structurées, Ann. Sci. École Norm. Sup. (3) 80 (1963), 349–426. 131, 760Google Scholar
282. Ehresmann, C., Catégories et structures, Dunod, Paris, 1965. 131, 760Google Scholar
283. Eilenberg, S., Automata, languages, and machines. Vol. B, Academic Press, New York-London, 1976, With two chapters by Bret Tilson, Pure and Applied Mathematics, Vol. 59. 494Google Scholar
284. Eilenberg, S. and Kelly, G. M., Closed categories, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965), Springer, New York, 1966, pp. 421–562. 735, 736, 737Google Scholar
285. Eilenberg, S. and Mac Lane, S., On the groups of H(Π, n). I, Ann. of Math. (2) 58 (1953), 55–106. 278Google Scholar
286. Eilenberg, S. and Moore, J. C., Adjoint functors and triples, Illinois J. Math. 9 (1965), 381–398. 760Google Scholar
287. Einziger, H., Incidence Hopf algebras: Antipodes, forest formulas, and noncrossing partitions, Ph.D. thesis, The George Washington University, 2010. 527Google Scholar
288. Eisenbud, D., Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995, With a view toward algebraic geometry. 279Google Scholar
289. Elduque, A. and Kochetov, M., Gradings on simple Lie algebras, Mathematical Surveys and Monographs, vol. 189, American Mathematical Society, Providence, RI; Atlantic Association for Research in the Mathematical Sciences (AARMS), Halifax, NS, 2013. 128, 673Google Scholar
290. Epstein, H., Trees, Nuclear Phys. B 912 (2016), 151–171. 71, 331Google Scholar
291. Epstein, H., Glaser, V. J., Stora, R., Geometry of the n point p space function of quantum field theory, Hyperfunctions and theoretical physics (Rencontre, Nice, 1973; dédié à la mémoire de A. Martineau), 1975, pp. 143–162. Lecture Notes in Math., Vol. 449. 71Google Scholar
292. Epstein, H., Glaser, V. J., Stora, R., General properties of the n-point functions in local quantum field theory, Structural analysis of collision amplitudes, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1976, Lectures delivered at Les Houches, École d’Été de Physique Théorique, 2-27 June 1975, pp. 7–94. 71, 331Google Scholar
293. Ernst, D. C., Cell complexes for arrangements with group actions, Master’s thesis, Northern Arizona University, 2000. 72Google Scholar
294. Espie, M., Novelli, J.-C., Racinet, G., Formal computations about multiple zeta values, From combinatorics to dynamical systems, IRMA Lect. Math. Theor. Phys., vol. 3, de Gruyter, Berlin, 2003, pp. 1–16. 333Google Scholar
295. Etingof, P., Gelaki, S., Nikshych, D., Ostrik, V., Tensor categories, Mathematical Surveys and Monographs, vol. 205, American Mathematical Society, Providence, RI, 2015. 233, 715Google Scholar
296. Etingof, P. and Schiffmann, O., Lectures on quantum groups, second ed., Lectures in Mathematical Physics, International Press, Somerville, MA, 2002. 129Google Scholar
297. Everitt, B. and Turner, P., Deletion-restriction for sheaf homology of geometric lattices, available at arXiv:1902.00399. 133Google Scholar
298. Everitt, B. and Turner, P., Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers, available at arXiv:1908.04500. 133Google Scholar
299. Eyre, T. M. W., Quantum stochastic calculus and representations of Lie superalgebras, Lecture Notes in Mathematics, vol. 1692, Springer-Verlag, Berlin, 1998. 281, 714Google Scholar
300. Fang, X., Generalized virtual braid groups, quasi-shuffle product and quantum groups, Int. Math. Res. Not. IMRN (2015), no. 6, 1717–1731. 281Google Scholar
301. Fang, X. and Jian, R.-Q., Cofree Hopf algebras on Hopf bimodule algebras, J. Pure Appl. Algebra 219 (2015), no. 9, 3913–3930. 281Google Scholar
302. Félix, Y., Halperin, S., Thomas, J.-C., Differential graded algebras in topology, Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 829–865. 279Google Scholar
303. Félix, Y., Halperin, S., Thomas, J.-C., Rational homotopy theory, Graduate Texts in Mathematics, vol. 205, Springer-Verlag, New York, 2001. 279, 675, 713, 715Google Scholar
304. Ferrer Santos, W. and Rittatore, A., Actions and invariants of algebraic groups, second ed., Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, FL, 2017. 128Google Scholar
305. Figueroa, H. and Gracia-Bondía, J. M., On the antipode of Kreimer’s Hopf algebra, available at arXiv:hep-th/9912170. 527Google Scholar
306. Finkelstein, D., On relations between commutators, Comm. Pure Appl. Math. 8 (1955), 245–250. 674Google Scholar
307. Flajolet, P. and Sedgewick, R., Analytic combinatorics, Cambridge University Press, Cambridge, 2009. 381Google Scholar
308. Foissy, L., Quantification de l’algèbre de Hopf de Malvenuto et Reutenauer, preprint 2005. 636Google Scholar
309. Foissy, L., Patras, F., Thibon, J.-Y., Deformations of shuffles and quasi-shuffles, Ann. Inst. Fourier (Grenoble) 66 (2016), no. 1, 209–237. 439, 608, 676, 713Google Scholar
310. Forcey, S., Siehler, J., Sowers, E. S., Operads in iterated monoidal categories, J. Homotopy Relat. Struct. 2 (2007), no. 1, 1–43. 736Google Scholar
311. Fox, T. F., Universal coalgebras, Ph.D. thesis, McGill University (Canada), 1976. 382, 441Google Scholar
312. Fox, T. F., The coalgebra enrichment of algebraic categories, Comm. Algebra 9 (1981), no. 3, 223–234. 382, 441Google Scholar
313. Fox, T. F., The tensor product of Hopf algebras, Rend. Istit. Mat. Univ. Trieste 24 (1992), no. 1-2, 65–71 (1994). 382Google Scholar
314. Fox, T. F., The construction of cofree coalgebras, J. Pure Appl. Algebra 84 (1993), no. 2, 191–198. 281Google Scholar
315. Franz, U. and Schott, R., Stochastic processes and operator calculus on quantum groups, Mathematics and its Applications, vol. 490, Kluwer Academic Publishers, Dordrecht, 1999. 130Google Scholar
316. Frappat, L., Sciarrino, A., Sorba, P., Dictionary on Lie algebras and superalgebras, Academic Press, Inc., San Diego, CA, 2000. 714Google Scholar
317. Frei, G. and Stammbach, U., Heinz Hopf, History of topology, North-Holland, Amsterdam, 1999, pp. 991–1008. 572Google Scholar
318. Fresse, B., Cogroups in algebras over an operad are free algebras, Comment. Math. Helv. 73 (1998), no. 4, 637–676. 574, 676, 716Google Scholar
319. Fresse, B., Lie theory of formal groups over an operad, J. Algebra 202 (1998), no. 2, 455–511. 716Google Scholar
320. Fresse, B., On the homotopy of simplicial algebras over an operad, Trans. Amer. Math. Soc. 352 (2000), no. 9, 4113–4141. 132, 278Google Scholar
321. Fresse, B., Koszul duality of operads and homology of partition posets, Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic K-theory, Contemp. Math., vol. 346, Amer. Math. Soc., Providence, RI, 2004, pp. 115–215. 203Google Scholar
322. Fresse, B., Théorie des opérades de Koszul et homologie des algèbres de Poisson, Ann. Math. Blaise Pascal 13 (2006), no. 2, 237–312. 675, 715Google Scholar
323. Fresse, B., Modules over operads and functors, Lecture Notes in Mathematics, vol. 1967, Springer-Verlag, Berlin, 2009. 203Google Scholar
324. Fresse, B., Homotopy of operads and Grothendieck-Teichmüller groups. Part 1, Mathematical Surveys and Monographs, vol. 217, American Mathematical Society, Providence, RI, 2017, The algebraic theory and its topological background. 131, 203, 278, 439, 526, 573, 676, 677, 716Google Scholar
325. Fresse, B., Homotopy of operads and Grothendieck-Teichmüller groups. Part 2, Mathematical Surveys and Monographs, vol. 217, American Mathematical Society, Providence, RI, 2017, The applications of (rational) homotopy theory methods. 203, 737Google Scholar
326. Freund, P. G. O., Introduction to supersymmetry, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1986. 673Google Scholar
327. Freyd, P. J., Abelian categories. An introduction to the theory of functors, Harper’s Series in Modern Mathematics, Harper & Row Publishers, New York, 1964. 493Google Scholar
328. Freyd, P. J. and Scedrov, A., Categories, allegories, North-Holland Mathematical Library, vol. 39, North-Holland Publishing Co., Amsterdam, 1990. 493Google Scholar
329. Friedrichs, K. O., Mathematical aspects of the quantum theory of fields. V. Fields modified by linear homogeneous forces, Comm. Pure Appl. Math. 6 (1953), 1–72. 674Google Scholar
330. Fröhlich, A., Formal groups, Lecture Notes in Mathematics, No. 74, Springer-Verlag, Berlin-New York, 1968. 128, 574, 714Google Scholar
331. Fuchs, J., Affine Lie algebras and quantum groups, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1995, An introduction, with applications in conformal field theory, Corrected reprint of the 1992 original. 129Google Scholar
332. Fulton, W., Young tableaux, London Mathematical Society Student Texts, vol. 35, Cambridge University Press, Cambridge, 1997, With applications to representation theory and geometry. 332Google Scholar
333. Gabriel, P., Sur les catégories abéliennes localement Noethériennes et leurs applications aux algèbres étudiées par Dieudonné, Séminaire J.–P. Serre, 1960. 128Google Scholar
334. Gabriel, P., Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323–448. 204Google Scholar
335. Gabriel, P., Exposé VII, Etude infinitesimale des schemas en groupes, Schémas en groupes. I: Propriétés générales des schémas en groupes, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics, Vol. 151, Springer-Verlag, Berlin-New York, 1970, pp. xv+564. 128, 232, 439, 468, 525, 712, 714, 715Google Scholar
336. Gabriel, P. and Zisman, M., Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer-Verlag New York, Inc., New York, 1967. 133, 760Google Scholar
337. Gaines, J. G., The algebra of iterated stochastic integrals, Stochastics Stochastics Rep. 49 (1994), no. 3-4, 169–179. 281, 676Google Scholar
338. Gaines, J. G., A basis for iterated stochastic integrals, Math. Comput. Simulation 38 (1995), no. 1-3, 7–11, Probabilités numériques (Paris, 1992). 281, 676Google Scholar
339. Garner, R., Understanding the small object argument, Appl. Categ. Structures 17 (2009), no. 3, 247–285. 203, 736Google Scholar
340. Garner, R. and López Franco, I., Commutativity, J. Pure Appl. Algebra 220 (2016), no. 5, 1707–1751. 736Google Scholar
341. Garsia, A. M., Combinatorics of the free Lie algebra and the symmetric group, Analysis, et cetera, Academic Press, Boston, MA, 1990, pp. 309–382. 440, 674Google Scholar
342. Garsia, A. M. and Reutenauer, C., A decomposition of Solomon’s descent algebra, Adv. Math. 77 (1989), no. 2, 189–262. 573Google Scholar
343. Gebhard, D. D. and Sagan, B. E., A chromatic symmetric function in noncommuting variables, J. Algebraic Combin. 13 (2001), no. 3, 227–255. 333Google Scholar
344. Geissinger, L., Hopf algebras of symmetric functions and class functions, Combinatoire et représentation du groupe symétrique (Actes Table Ronde C.N.R.S., Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976), Springer, Berlin, 1977, pp. 168–181. Lecture Notes in Math., Vol. 579. 129, 332Google Scholar
345. Gelfand, I. M., The center of an infinitesimal group ring, Mat. Sbornik N.S. 26(68) (1950), 103–112. 673, 712Google Scholar
346. Gelfand, I. M., Center of the infinitesimal group ring, Collected papers. Vol. II, Edited by S. G. Gindikin, V. W. Guillemin, A. A. Kirillov, B. Kostant and S. Sternberg, Springer-Verlag, Berlin, 1988, pp. 22–30. 673, 712Google Scholar
347. Gelfand, I. M., Krob, D., Lascoux, A., Leclerc, B., Retakh, V. S., Thibon, J.-Y., Noncommutative symmetric functions, Adv. Math. 112 (1995), no. 2, 218–348. 333, 527, 607, 712Google Scholar
348. Gerstenhaber, M., The cohomology structure of an associative ring, Ann. of Math. (2) 78 (1963), 267–288. 672Google Scholar
349. Gerstenhaber, M. and Schack, S. D., The shuffle bialgebra and the cohomology of commutative algebras, J. Pure Appl. Algebra 70 (1991), no. 3, 263–272. 278, 468Google Scholar
350. Gessel, I. M., Multipartite P -partitions and inner products of skew Schur functions, Combinatorics and algebra (Boulder, Colo., 1983), Amer. Math. Soc., Providence, RI, 1984, pp. 289–317. 333Google Scholar
351. Getzler, E. and Jones, J. D. S., Operads, homotopy algebra and iterated integrals for double loop spaces, available at arXiv:hep-th/9403055. 203Google Scholar
352. Giachetta, G., Mangiarotti, L., Sardanashvily, G., Geometric and algebraic topological methods in quantum mechanics, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. 383Google Scholar
353. Ginsburg, S. and Spanier, E. H., Mappings of languages by two-tape devices, J. Assoc. Comput. Mach. 12 (1965), 423–434. 278Google Scholar
354. Ginzburg, V. and Kapranov, M., Koszul duality for operads, Duke Math. J. 76 (1994), no. 1, 203–272. 203Google Scholar
355. Ginzburg, V. and Schedler, T., Differential operators and BV structures in noncommutative geometry, Selecta Math. (N.S.) 16 (2010), no. 4, 673–730. 132Google Scholar
356. Godement, R., Topologie algébrique et théorie des faisceaux, Actualit’es Sci. Ind. No. 1252. Publ. Math. Univ. Strasbourg. No. 13, Hermann, Paris, 1958. 760Google Scholar
357. Godement, R., Introduction to the theory of Lie groups, Universitext, Springer, Cham, 2017, Translated from the 2004 French edition by Urmie Ray. 713Google Scholar
358. Goerss, P. G., Barratt’s desuspension spectral sequence and the Lie ring analyzer, Quart. J. Math. Oxford Ser. (2) 44 (1993), no. 173, 43–85. 676Google Scholar
359. Goncharov, A. B., Periods and mixed motives, available at arXiv:math/0202154. 333Google Scholar
360. Gordon, R. and Power, J., Enrichment through variation, J. Pure Appl. Algebra 120 (1997), no. 2, 167–185. 730Google Scholar
361. Gould, M. D., Zhang, R. B., Bracken, A. J., Quantum double construction for graded Hopf algebras, Bull. Austral. Math. Soc. 47 (1993), no. 3, 353–375. 130Google Scholar
362. Goyvaerts, I. and Vercruysse, J., A note on the categorification of Lie algebras, Lie theory and its applications in physics, Springer Proc. Math. Stat., vol. 36, Springer, Tokyo, 2013, pp. 541–550. 675, 676, 677Google Scholar
363. Goyvaerts, I. and Vercruysse, J., Lie monads and dualities, J. Algebra 414 (2014), 120–158. 675, 677Google Scholar
364. Gracia-Bondía, J. M., Várilly, J. C., Figueroa, H., Elements of noncommutative geometry, Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser Boston, Inc., Boston, MA, 2001. 129, 381, 383, 527, 714Google Scholar
365. Grandis, M., Directed algebraic topology, New Mathematical Monographs, vol. 13, Cambridge University Press, Cambridge, 2009, Models of non-reversible worlds. 761Google Scholar
366. Grandis, M., Category theory and applications, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2018, A textbook for beginners. 760Google Scholar
367. Grandis, M., Higher dimensional categories: from double to multiple categories, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2019. 760Google Scholar
368. Gray, B., Homotopy theory, Academic Press, New York-London, 1975, An introduction to algebraic topology, Pure and Applied Mathematics, Vol. 64. 132Google Scholar
369. Gray, J. W., Formal category theory: adjointness for 2-categories, Lecture Notes in Mathematics, Vol. 391, Springer-Verlag, Berlin-New York, 1974. 760, 761Google Scholar
370. Green, H. S. and Jarvis, P. D., Casimir invariants, characteristic identities, and Young diagrams for color algebras and superalgebras, J. Math. Phys. 24 (1983), no. 7, 1681– 1687. 673Google Scholar
371. Green, J. A., Quantum groups, Hall algebras and quantized shuffles, Finite reductive groups (Luminy, 1994), Progr. Math., vol. 141, Birkhäuser Boston, Boston, MA, 1997, pp. 273–290. 281Google Scholar
372. Greene, C., On the Möbius algebra of a partially ordered set, Advances in Math. 10 (1973), 177–187. 71Google Scholar
373. Griffing, G., Cofree Lie and other nonassociative coalgebras, Ph.D. thesis, University of California, Riverside, 1986. 281, 675Google Scholar
374. Griffing, G., The cofree nonassociative coalgebra, Comm. Algebra 16 (1988), no. 11, 2387– 2414. 281Google Scholar
375. Griffing, G., A nonisomorphism theorem for cofree Lie coalgebras, J. Algebra 115 (1988), no. 2, 431–441. 675Google Scholar
376. Griffiths, P. and Morgan, J. W., Rational homotopy theory and differential forms, second ed., Progress in Mathematics, vol. 16, Springer, New York, 2013. 439Google Scholar
377. Grinberg, D. and Reiner, V., Hopf algebras in combinatorics, available at arXiv:1409.8356. 129, 333, 440, 526, 527, 572, 636Google Scholar
378. Grivel, P.-P., Une histoire du théorème de Poincaré-Birkhoff-Witt, Expo. Math. 22 (2004), no. 2, 145–184. 712, 716Google Scholar
379. Grothendieck, A. and Verdier, J.-L., Théorie des topos et cohomologie étale des schémas. Tome 1: Théorie des topos, Lecture Notes in Mathematics, Vol. 269, Springer-Verlag, Berlin-New York, 1972, Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4), Dirigé par M. Artin, A. Grothendieck, et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. 493Google Scholar
380. Grove, L. C. and Benson, C. T., Finite reflection groups, second ed., Graduate Texts in Mathematics, vol. 99, Springer-Verlag, New York, 1985. 72Google Scholar
381. Grünbaum, B., Arrangements of hyperplanes, Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing, Louisiana State Univ., Baton Rouge, La., 1971, pp. 41–106. 72Google Scholar
382. Grünbaum, B., Convex polytopes, second ed., Graduate Texts in Mathematics, vol. 221, Springer-Verlag, New York, 2003, Prepared and with a preface by Volker Kaibel, Victor Klee and Günter M. Ziegler. 72Google Scholar
383. Grünenfelder, L. A., Über die struktur von Hopf-algebren, Ph.D. thesis, ETH-Zurich, 1969. 232, 233, 234, 525, 526, 674, 714, 715Google Scholar
384. Grünenfelder, L. A., Hopf-algebren und coradikal, Math. Z. 116 (1970), 166–182. 232, 525, 674, 714, 715Google Scholar
385. Grünenfelder, L. A., (Co-)homology of commutative coalgebras, Comm. Algebra 16 (1988), no. 3, 541–576. 573Google Scholar
386. Grünenfelder, L. A., About braided and ordinary Hopf algebras, Milan J. Math. 71 (2003), 121– 140. 715Google Scholar
387. Grünenfelder, L. A. and Mastnak, M., On bimeasurings, J. Pure Appl. Algebra 204 (2006), no. 2, 258–269. 129, 382Google Scholar
388. Grünenfelder, L. A. and Mastnak, M., On bimeasurings. II, J. Pure Appl. Algebra 209 (2007), no. 3, 823–832. 382Google Scholar
389. Grünenfelder, L. A. and Paré, R., Families parametrized by coalgebras, J. Algebra 107 (1987), no. 2, 316–375. 382Google Scholar
390. Gugenheim, V. K. A. M., On extensions of algebras, co-algebras and Hopf algebras. I, Amer. J. Math. 84 (1962), 349–382. 128Google Scholar
391. Guichardet, A., Groupes quantiques, Savoirs Actuels, InterEditions, Paris; CNRS Éditions, Paris, 1995, Introduction au point de vue formel. 129, 278Google Scholar
392. Guillemin, V. W. and Sternberg, S., Supersymmetry and equivariant de Rham theory, Mathematics Past and Present, Springer-Verlag, Berlin, 1999, With an appendix containing two reprints by Henri Cartan. 130Google Scholar
393. Guo, L., An introduction to Rota-Baxter algebra, Surveys of Modern Mathematics, vol. 4, International Press, Somerville, MA; Higher Education Press, Beijing, 2012. 281Google Scholar
394. Guo, L. and Keigher, W., Baxter algebras and shuffle products, Adv. Math. 150 (2000), no. 1, 117–149. 280Google Scholar
395. Guo, L. and Xie, B., Structure theorems of mixable shuffle algebras, Comm. Algebra 41 (2013), no. 7, 2629–2649. 676Google Scholar
396. Gurevich, D. I., Generalized translation operators on Lie groups, Izv. Akad. Nauk Armyan. SSR Ser. Mat. 18 (1983), no. 4, 305–317. 677Google Scholar
397. Gurevich, D. I., Elements of formal Lie theory and the Poincaré-Birkhoff-Witt theorem for generalized shift operators, Funktsional. Anal. i Prilozhen. 20 (1986), no. 4, 72–73. 677Google Scholar
398. Gurevich, D. I., The Yang-Baxter equation and a generalization of formal Lie theory, Dokl. Akad. Nauk SSSR 288 (1986), no. 4, 797–801. 716Google Scholar
399. Gurevich, D. I., Algebraic aspects of the quantum Yang-Baxter equation, Algebra i Analiz 2 (1990), no. 4, 119–148. 131Google Scholar
400. Gurski, N., Coherence in three-dimensional category theory, Cambridge Tracts in Mathematics, vol. 201, Cambridge University Press, Cambridge, 2013. 761Google Scholar
401. Hackney, P., Robertson, M., Yau, D., Infinity properads and infinity wheeled properads, Lecture Notes in Mathematics, vol. 2147, Springer, Cham, 2015. 203Google Scholar
402. Hadamard, J. S., Théorème sur les séries entières, Acta Math. 22 (1899), no. 1, 55–63. 381Google Scholar
403. Haiman, M. and Schmitt, W. R., Incidence algebra antipodes and Lagrange inversion in one and several variables, J. Combin. Theory Ser. A 50 (1989), no. 2, 172–185. 526Google Scholar
404. Hain, R. M., Iterated integrals, minimal models and rational homotopy theory, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1980. 279, 714Google Scholar
405. Hain, R. M., Iterated integrals and homotopy periods, Mem. Amer. Math. Soc. 47 (1984), no. 291, iv+98. 279, 573, 675, 714Google Scholar
406. Hain, R. M., On the indecomposable elements of the bar construction, Proc. Amer. Math. Soc. 98 (1986), no. 2, 312–316. 279, 572Google Scholar
407. Hain, R. M., The de Rham homotopy theory of complex algebraic varieties. I, K-Theory 1 (1987), no. 3, 271–324. 439Google Scholar
408. Hall, B., Lie groups, Lie algebras, and representations, second ed., Graduate Texts in Mathematics, vol. 222, Springer, Cham, 2015, An elementary introduction. 713Google Scholar
409. Hall, P., A Contribution to the Theory of Groups of Prime-Power Order, Proc. London Math. Soc. (2) 36 (1934), 29–95. 674Google Scholar
410. Hall, P., The Eulerian functions of a group, Quarterly J. Math. 7 (1936), no. 1, 134– 151. 71Google Scholar
411. Halmos, P. R., Finite-dimensional vector spaces, The University Series in Undergraduate Mathematics, D. Van Nostrand Co., Inc., Princeton-Toronto-New York-London, 1958, 2nd ed. 381Google Scholar
412. Halpern, E., On the structure of hyperalgebras. Class 1 Hopf algebras, Portugal. Math. 17 (1958), 127–147. 128, 232, 233, 572, 573Google Scholar
413. Halpern, E., Twisted polynomial hyperalgebras, Mem. Amer. Math. Soc. no. 29 (1958), 61 pp. (1958). 128, 573Google Scholar
414. Halpern, E., A note on divided powers in a Hopf algebra, Proc. Amer. Math. Soc. 11 (1960), 547–556. 572, 573Google Scholar
415. Halpern, E., On the primitivity of Hopf algebras over a field with prime characteristic, Proc. Amer. Math. Soc. 11 (1960), 117–126. 128, 233, 573Google Scholar
416. Harish-Chandra, On representations of Lie algebras, Ann. of Math. (2) 50 (1949), 900–915. 673, 712Google Scholar
417. Harish-Chandra, On some applications of the universal enveloping algebra of a semisimple Lie algebra, Trans. Amer. Math. Soc. 70 (1951), 28–96. 673Google Scholar
418. Harish-Chandra, Representations of a semisimple Lie group on a Banach space. I, Trans. Amer. Math. Soc. 75 (1953), 185–243. 712Google Scholar
419. Harper, J. R., Secondary cohomology operations, Graduate Studies in Mathematics, vol. 49, American Mathematical Society, Providence, RI, 2002. 128Google Scholar
420. Hasse, M. and Michler, L., Theorie der Kategorien, Mathematische Monographien, Band 7, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. 131Google Scholar
421. Hatcher, A., Algebraic topology, Cambridge University Press, Cambridge, 2002. 572Google Scholar
422. Hazewinkel, M., Introductory recommendations for the study of Hopf algebras in mathematics and physics, CWI Quarterly 4 (1991), no. 1, 3–26. 129Google Scholar
423. Hazewinkel, M., Generalized overlapping shuffle algebras, J. Math. Sci. (New York) 106 (2001), no. 4, 3168–3186, Pontryagin Conference, 8, Algebra (Moscow, 1998). 280Google Scholar
424. Hazewinkel, M., Cofree coalgebras and multivariable recursiveness, J. Pure Appl. Algebra 183 (2003), no. 1-3, 61–103. 281Google Scholar
425. Hazewinkel, M., Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions, Acta Appl. Math. 75 (2003), no. 1-3, 55–83, Monodromy and differential equations (Moscow, 2001). 333, 636Google Scholar
426. Hazewinkel, M., Symmetric functions, noncommutative symmetric functions and quasisymmetric functions. II, Acta Appl. Math. 85 (2005), no. 1-3, 319–340. 333, 676Google Scholar
427. Hazewinkel, M., Formal groups and applications, AMS Chelsea Publishing, Providence, RI, 2012, Corrected reprint of the 1978 original. 128, 279, 333, 381, 440, 526, 714Google Scholar
428. Hazewinkel, M., Gubareni, N., Kirichenko, V. V., Algebras, rings and modules, Mathematical Surveys and Monographs, vol. 168, American Mathematical Society, Providence, RI, 2010, Lie algebras and Hopf algebras. 129, 278, 332, 333, 383, 526, 527, 572, 636, 674Google Scholar
429. Helgason, S., Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. 713Google Scholar
430. Helmstetter, J., Série de Hausdorff d’une algèbre de Lie et projections canoniques dans l’algèbre enveloppante, J. Algebra 120 (1989), no. 1, 170–199. 440, 712, 714Google Scholar
431. Heyneman, R. G. and Radford, D. E., Reflexivity and coalgebras of finite type, J. Algebra 28 (1974), 215–246. 233Google Scholar
432. Heyneman, R. G. and Sweedler, M. E., Affine Hopf algebras. I, J. Algebra 13 (1969), 192–241. 233, 381, 525, 526, 715Google Scholar
433. Heyneman, R. G. and Sweedler, M. E., Affine Hopf algebras. II, J. Algebra 16 (1970), 271–297. 281, 573Google Scholar
434. Higgins, P. J., Baer invariants and the Birkhoff-Witt theorem, J. Algebra 11 (1969), 469–482. 712Google Scholar
435. Hilgert, J. and Neeb, K.-H., Structure and geometry of Lie groups, Springer Monographs in Mathematics, Springer, New York, 2012. 713Google Scholar
436. Hilton, P. J., Homotopy theory and duality, Gordon and Breach Science Publishers, New York-London-Paris, 1965. 132Google Scholar
437. Hilton, P. J., Heinz Hopf, Bull. London Math. Soc. 4 (1972), 202–217. 572Google Scholar
438. Hilton, P. J. and Stammbach, U., A course in homological algebra, second ed., Graduate Texts in Mathematics, vol. 4, Springer-Verlag, New York, 1997. 712Google Scholar
439. Hobst, D. and Pareigis, B., Double quantum groups, J. Algebra 242 (2001), no. 2, 460–494. 761Google Scholar
440. Hochschild, G. P., Algebraic Lie algebras and representative functions, Illinois J. Math. 3 (1959), 499–523. 676Google Scholar
441. Hochschild, G. P., Representation theory of Lie algebras, Technical Report, The University of Chicago, 1959, Lectures by G. Hochschild. Notes by G. Leger. 676, 713Google Scholar
442. Hochschild, G. P., The structure of Lie groups, Holden-Day, Inc., San Francisco-London-Amsterdam, 1965. 128, 440, 525, 674, 713Google Scholar
443. Hochschild, G. P., Algebraic groups and Hopf algebras, Illinois J. Math. 14 (1970), 52–65. 128, 676Google Scholar
444. Hochschild, G. P., Introduction to affine algebraic groups, Holden-Day, Inc., San Francisco, Calif.-Cambridge-Amsterdam, 1971. 128, 381, 440, 525, 572Google Scholar
445. Hochschild, G. P., Basic theory of algebraic groups and Lie algebras, Graduate Texts in Mathematics, vol. 75, Springer-Verlag, New York-Berlin, 1981. 128, 234, 381, 440, 525, 572, 676, 713, 715Google Scholar
446. Hochschild, G. P. and Mostow, G. D., Complex analytic groups and Hopf algebras, Amer. J. Math. 91 (1969), 1141–1151. 128, 525Google Scholar
447. Hochschild, G. P. and Mostow, G. D., Pro-affine algebraic groups, Amer. J. Math. 91 (1969), 1127–1140. 128Google Scholar
448. Hoffman, M. E., The algebra of multiple harmonic series, J. Algebra 194 (1997), no. 2, 477–495. 333Google Scholar
449. Hoffman, M. E., Quasi-shuffle products, J. Algebraic Combin. 11 (2000), no. 1, 49–68. 280, 526, 607, 676Google Scholar
450. Hoffman, M. E. and Ihara, K., Quasi-shuffle products revisited, J. Algebra 481 (2017), 293–326. 280, 281, 441, 526, 608Google Scholar
451. Hoffman, M. E. and Ohno, Y., Relations of multiple zeta values and their algebraic expression, J. Algebra 262 (2003), no. 2, 332–347. 333Google Scholar
452. Hofmann, K. H., The duality of compact semigroups and C∗-bigebras, Lecture Notes in Mathematics, Vol. 129, Springer-Verlag, Berlin-New York, 1970. 131Google Scholar
453. Hofmann, K. H. and Morris, S. A., The structure of compact groups, De Gruyter Studies in Mathematics, vol. 25, De Gruyter, Berlin, 2013, A primer for the student—a handbook for the expert, Third edition, revised and augmented. 131, 572, 573Google Scholar
454. Honda, T., Formal groups and zeta-functions, Osaka Math. J. 5 (1968), 199–213. 574Google Scholar
455. Honda, T., On the theory of commutative formal groups, J. Math. Soc. Japan 22 (1970), 213–246. 574Google Scholar
456. Hong, J. and Kang, S.-J., Introduction to quantum groups and crystal bases, Graduate Studies in Mathematics, vol. 42, American Mathematical Society, Providence, RI, 2002. 713Google Scholar
457. Hopf, H., Sur la topologie des groupes clos de Lie et de leurs généralisations, C. R. Acad. Sci. Paris 208 (1939), 1266–1267. 571Google Scholar
458. Hopf, H., Über die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallge-meinerungen, Ann. of Math. (2) 42 (1941), 22–52. 127, 232, 571, 573Google Scholar
459. Hopf, H., Selecta Heinz Hopf, Herausgegeben zu seinem 70. Geburtstag von der Eid-genössischen Technischen Hochschule Zürich, Springer-Verlag, Berlin-New York, 1964. 571Google Scholar
460. Hopf, H., Collected papers/Gesammelte Abhandlungen, Springer Collected Works in Mathematics, Springer, Heidelberg, 2013, Edited and with a preface and foreword by Beno Eckmann, With appendices by Peter J. Hilton, P. Alexandroff, Eckmann and Hopf. Reprint of the 2001 edition. 571, 572Google Scholar
461. Horn, R. A., The Hadamard product, Matrix theory and applications (Phoenix, AZ, 1989), Proc. Sympos. Appl. Math., vol. 40, Amer. Math. Soc., Providence, RI, 1990, pp. 87–169. 381Google Scholar
462. Horn, R. A. and Johnson, C. R., Topics in matrix analysis, Cambridge University Press, Cambridge, 1994, Corrected reprint of the 1991 original. 381Google Scholar
463. Hovey, M., Model categories, Mathematical Surveys and Monographs, vol. 63, American Mathematical Society, Providence, RI, 1999. 736Google Scholar
464. Hubbuck, J. R., A Hopf algebra decomposition theorem, Bull. London Math. Soc. 13 (1981), no. 2, 125–128. 468Google Scholar
465. Huber, P. J., Homotopy theory in general categories, Math. Ann. 144 (1961), 361–385. 760Google Scholar
466. Hudson, R. L., The Z2-graded sticky shuffle product Hopf algebra, Quantum probability, Banach Center Publ., vol. 73, Polish Acad. Sci. Inst. Math., Warsaw, 2006, pp. 237–243. 281Google Scholar
467. Hudson, R. L., Hopf-algebraic aspects of iterated stochastic integrals, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12 (2009), no. 3, 479–496. 281, 526, 714Google Scholar
468. Hudson, R. L., Sticky shuffle product Hopf algebras and their stochastic representations, New trends in stochastic analysis and related topics, Interdiscip. Math. Sci., vol. 12, World Sci. Publ., Hackensack, NJ, 2012, pp. 165–181. 281, 526, 714Google Scholar
469. Hudson, R. L. and Parthasarathy, K. R., The Casimir chaos map for U(N), Tatra Mt. Math. Publ. 3 (1993), 81–88, Measure theory (Liptovský Ján, 1993). 281Google Scholar
470. Hudson, R. L. and Parthasarathy, K. R., Chaos map for the universal enveloping algebra of U(N), Math. Proc. Cambridge Philos. Soc. 117 (1995), no. 1, 21–30. 714Google Scholar
471. Hudson, R. L. and Pulmannová, S., Double product integrals and Enriquez quantization of Lie bialgebras. I. The quasitriangular identities, J. Math. Phys. 45 (2004), no. 5, 2090–2105. 281, 714Google Scholar
472. Humpert, B. and Martin, J. L., The incidence Hopf algebra of graphs, SIAM J. Discrete Math. 26 (2012), no. 2, 555–570. 527Google Scholar
473. Humphreys, J. E., Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, vol. 9, Springer-Verlag, New York-Berlin, 1978, Second printing, revised. 713Google Scholar
474. Humphreys, J. E., Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge, 1990. 72Google Scholar
475. Hyland, M., López Franco, I., Vasilakopoulou, C., Hopf measuring comonoids and enrichment, Proc. Lond. Math. Soc. (3) 115 (2017), no. 5, 1118–1148. 381, 382, 383, 730, 737Google Scholar
476. Ihara, K., Kajikawa, J., Ohno, Y., Okuda, J.-i., Multiple zeta values vs. multiple zeta-star values, J. Algebra 332 (2011), 187–208. 280, 608Google Scholar
477. Ihara, K., Kaneko, M., Zagier, D., Derivation and double shuffle relations for multiple zeta values, Compos. Math. 142 (2006), no. 2, 307–338. 333Google Scholar
478. Ismail, F. M., Exponentielle et groupes de Lie gradués, Ph.D. thesis, Université de Grenoble, 1982. 440, 714Google Scholar
479. Jacobson, N., Rational methods in the theory of Lie algebras, Ann. of Math. (2) 36 (1935), no. 4, 875–881. 671, 673Google Scholar
480. Jacobson, N., Lie algebras, Dover Publications, Inc., New York, 1979, Republication of the 1962 original. 674, 675, 713Google Scholar
481. Jacobson, N., Basic algebra. II, second ed., W. H. Freeman and Company, New York, 1989. 129, 674Google Scholar
482. Jambu, M., Arrangements d’hyperplans. I. Les groupes de réflexions, Ann. Sci. Math. Québec 12 (1988), no. 1, 73–99. 72Google Scholar
483. Janelidze, G. and Kelly, G. M., A note on actions of a monoidal category, vol. 9, 2001/02, CT2000 Conference (Como), pp. 61–91. 730, 736, 737Google Scholar
484. Jantzen, J. C., Representations of algebraic groups, second ed., Mathematical Surveys and Monographs, vol. 107, American Mathematical Society, Providence, RI, 2003. 128Google Scholar
485. Jian, R.-Q., From quantum quasi-shuffle algebras to braided Rota-Baxter algebras, Lett. Math. Phys. 103 (2013), no. 8, 851–863. 281Google Scholar
486. Jian, R.-Q., Quantum quasi-shuffle algebras II, J. Algebra 472 (2017), 480–506. 281Google Scholar
487. Jian, R.-Q. and Rosso, M., Braided cofree Hopf algebras and quantum multi-brace algebras, J. Reine Angew. Math. 667 (2012), 193–220. 281Google Scholar
488. Jian, R.-Q., Rosso, M., Zhang, J., Quantum quasi-shuffle algebras, Lett. Math. Phys. 92 (2010), no. 1, 1–16. 281Google Scholar
489. Jimbo, M., A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), no. 1, 63–69. 129Google Scholar
490. Jimbo, M., A q-analogue of U(gl(N +1)), Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no. 3, 247–252. 129Google Scholar
491. Johnstone, P. T., Adjoint lifting theorems for categories of algebras, Bull. London Math. Soc. 7 (1975), no. 3, 294–297. 761Google Scholar
492. Johnstone, P. T., Topos theory, Academic Press, London-New York, 1977, London Mathematical Society Monographs, Vol. 10. 761Google Scholar
493. Johnstone, P. T., Sketches of an elephant: a topos theory compendium. Vol. 1, Oxford Logic Guides, vol. 43, The Clarendon Press, Oxford University Press, New York, 2002. 494, 736, 737, 760, 761Google Scholar
494. Jonah, D. W., Cohomology of coalgebras, Ph.D. thesis, Brown University, 1967. 131Google Scholar
495. Jonah, D. W., Cohomology of coalgebras, Memoirs of the American Mathematical Society, No. 82, American Mathematical Society, Providence, RI, 1968. 131Google Scholar
496. Joni, S. A. and Rota, G.-C., Coalgebras and bialgebras in combinatorics, Umbral calculus and Hopf algebras (Norman, Okla., 1978), Contemp. Math., vol. 6, Amer. Math. Soc., Providence, RI, 1982, pp. 1–47. 129, 332Google Scholar
497. Joseph, A., Quantum groups and their primitive ideals, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 29, Springer-Verlag, Berlin, 1995. 129Google Scholar
498. Joyal, A., Une théorie combinatoire des séries formelles, Adv. in Math. 42 (1981), no. 1, 1–82. 131, 132, 203, 282Google Scholar
499. Joyal, A., Lettre d’André Joyal à Alexandre Grothendieck, editée par Georges Maltsiniotis, 1984, available at https://webusers.imj-prg.fr/~georges.maltsiniotis/ps. html. 735Google Scholar
500. Joyal, A., Foncteurs analytiques et espèces de structures, Combinatoire énumérative (Montreal, Que., 1985/Quebec, Que., 1985), Lecture Notes in Math., vol. 1234, Springer, Berlin, 1986, pp. 126–159. 131, 132, 676, 715Google Scholar
501. Joyal, A. and Street, R., Braided monoidal categories, Macquarie University, 1986, Report No. 860081. 133, 735Google Scholar
502. Joyal, A. and Street, R., The geometry of tensor calculus. I, Adv. Math. 88 (1991), no. 1, 55–112. 736Google Scholar
503. Joyal, A. and Street, R., Braided tensor categories, Adv. Math. 102 (1993), no. 1, 20–78. 133, 736Google Scholar
504. Kac, G. I., A generalization of the principle of duality for groups, Dokl. Akad. Nauk SSSR 138 (1961), 275–278. 128Google Scholar
505. Kac, G. I., Ring groups and the duality principle, Trudy Moskov. Mat. Obšč. 12 (1963), 259–301. 128Google Scholar
506. Kac, V. G., Lie superalgebras, Advances in Math. 26 (1977), no. 1, 8–96. 713Google Scholar
507. Kamps, K. H. and Porter, T., Abstract homotopy and simple homotopy theory, World Scientific Publishing Co., Inc., River Edge, NJ, 1997. 737Google Scholar
508. Kane, R., The homology of Hopf spaces, North-Holland Mathematical Library, vol. 40, North-Holland Publishing Co., Amsterdam, 1988. 128, 232, 233, 279, 572Google Scholar
509. Kane, R., Reflection groups and invariant theory, CMS Books in Mathematics, vol. 5, Springer-Verlag, New York, 2001. 72Google Scholar
510. Kaplansky, I., Bialgebras, University of Chicago Lecture Notes, 1975. 129, 233, 525, 714Google Scholar
511. Karaali, G., On Hopf algebras and their generalizations, Comm. Algebra 36 (2008), no. 12, 4341–4367. 129Google Scholar
512. Karoubi, M., Algèbres de Clifford et K-théorie, Ann. Sci. École Norm. Sup. (4) 1 (1968), 161–270. 493Google Scholar
513. Karoubi, M., K-theory, Classics in Mathematics, Springer-Verlag, Berlin, 2008, An introduction, Reprint of the 1978 edition, With a new postface by the author and a list of errata. 483, 493Google Scholar
514. Kashina, Y., A generalized power map for Hopf algebras, Hopf algebras and quantum groups (Brussels, 1998), Lecture Notes in Pure and Appl. Math., vol. 209, Dekker, New York, 2000, pp. 159–175. 468Google Scholar
515. Kashina, Y., Montgomery, S., Ng, S.-H., On the trace of the antipode and higher indicators, Israel J. Math. 188 (2012), 57–89. 468Google Scholar
516. Kashina, Y., Sommerhäuser, Y., Zhu, Y., On higher Frobenius-Schur indicators, Mem. Amer. Math. Soc. 181 (2006), no. 855, viii+65. 468Google Scholar
517. Kassel, C., Quantum groups, Graduate Texts in Mathematics, vol. 155, Springer-Verlag, New York, 1995. 129, 278, 332, 381, 383, 526, 713, 736Google Scholar
518. Kassel, C., Rosso, M., Turaev, V., Quantum groups and knot invariants, Panoramas et Synthèses, vol. 5, Société Mathématique de France, Paris, 1997. 278Google Scholar
519. Kaufmann, R. M. and Ward, B. C., Feynman categories, Astérisque (2017), no. 387, vii+161. 203Google Scholar
520. Kelly, G. M., On MacLane’s conditions for coherence of natural associativities, com-mutativities, etc, J. Algebra 1 (1964), 397–402. 735Google Scholar
521. Kelly, G. M., Adjunction for enriched categories, Reports of the Midwest Category Seminar, III, Springer, Berlin, 1969, pp. 166–177. 737, 761Google Scholar
522. Kelly, G. M., Doctrinal adjunction, Category Seminar (Proc. Sem., Sydney, 1972/1973), Springer, Berlin, 1974, pp. 257–280. Lecture Notes in Math., Vol. 420. 761Google Scholar
523. Kelly, G. M., Basic concepts of enriched category theory, Repr. Theory Appl. Categ. (2005), no. 10, vi+137, Reprint of the 1982 original [Cambridge Univ. Press, Cambridge]. 725, 736, 737Google Scholar
524. Kelly, G. M., On the operads of J. P. May, Repr. Theory Appl. Categ. (2005), no. 13, 1–13. 132, 203Google Scholar
525. Kelly, G. M. and Street, R., Review of the elements of 2-categories, Category Seminar (Proc. Sem., Sydney, 1972/1973), Springer, Berlin, 1974, pp. 75–103. Lecture Notes in Math., Vol. 420. 760, 761Google Scholar
526. Khalkhali, M., Basic noncommutative geometry, second ed., EMS Series of Lectures in Mathematics, European Mathematical Society (EMS), Zürich, 2013. 129, 383, 715Google Scholar
527. Kharchenko, V. K., Quantum Lie algebras and related problems, Proceedings of the Third International Algebra Conference (Tainan, 2002), Kluwer Acad. Publ., Dordrecht, 2003, pp. 67–114. 278Google Scholar
528. Kharchenko, V. K., Connected braided Hopf algebras, J. Algebra 307 (2007), no. 1, 24–48. 279, 716Google Scholar
529. Kharchenko, V. K., Quantum Lie theory, Lecture Notes in Mathematics, vol. 2150, Springer, Cham, 2015, A multilinear approach. 130, 131, 232, 281, 673, 677, 713, 714, 716Google Scholar
530. Kharchenko, V. K. and Shestakov, I. P., Generalizations of Lie algebras, Adv. Appl. Clifford Algebr. 22 (2012), no. 3, 721–743. 677, 716Google Scholar
531. Kimura, N., The structure of idempotent semigroups. I, Pacific J. Math. 8 (1958), 257–275. 23Google Scholar
532. Kirillov, A., Jr., An introduction to Lie groups and Lie algebras, Cambridge Studies in Advanced Mathematics, vol. 113, Cambridge University Press, Cambridge, 2008. 713Google Scholar
533. Kleeman, R., Commutation factors on generalized Lie algebras, J. Math. Phys. 26 (1985), no. 10, 2405–2412. 673Google Scholar
534. Kleisli, H., Every standard construction is induced by a pair of adjoint functors, Proc. Amer. Math. Soc. 16 (1965), 544–546. 760Google Scholar
535. Klimyk, A. and Schmüdgen, K., Quantum groups and their representations, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1997. 129, 278, 381, 526Google Scholar
536. Knapp, A. W., Representation theory of semisimple groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 2001, An overview based on examples, Reprint of the 1986 original. 712Google Scholar
537. Knapp, A. W., Lie groups beyond an introduction, second ed., Progress in Mathematics, vol. 140, Birkhäuser Boston, Inc., Boston, MA, 2002. 713Google Scholar
538. Kock, J., Frobenius algebras and 2D topological quantum field theories, London Mathematical Society Student Texts, vol. 59, Cambridge University Press, Cambridge, 2004. 131, 133, 736Google Scholar
539. Kock, J., Note on commutativity in double semigroups and two-fold monoidal categories, J. Homotopy Relat. Struct. 2 (2007), no. 2, 217–228. 133, 736Google Scholar
540. Kostant, B., Groups over Z, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, RI, 1966, pp. 90–98. 381, 525Google Scholar
541. Kostant, B., Graded manifolds, graded Lie theory, and prequantization, Differential geometrical methods in mathematical physics (Proc. Sympos., Univ. Bonn, Bonn, 1975), Springer, Berlin, 1977, pp. 177–306. Lecture Notes in Math., Vol. 570. 130, 713, 714, 715Google Scholar
542. Koszul, J.-L., Homologie et cohomologie des algèbres de Lie, Bull. Soc. Math. France 78 (1950), 65–127. 232, 572, 573Google Scholar
543. Koszul, J.-L., Graded manifolds and graded Lie algebras, Proceedings of the international meeting on geometry and physics (Florence, 1982), Pitagora, Bologna, 1983, pp. 71– 84. 714Google Scholar
544. Kozlov, D., Combinatorial algebraic topology, Algorithms and Computation in Mathematics, vol. 21, Springer, Berlin, 2008. 204Google Scholar
545. Kreimer, D., On the Hopf algebra structure of perturbative quantum field theories, Adv. Theor. Math. Phys. 2 (1998), no. 2, 303–334. 527Google Scholar
546. Kreimer, D., Knots and Feynman diagrams, Cambridge Lecture Notes in Physics, vol. 13, Cambridge University Press, Cambridge, 2000. 527Google Scholar
547. Kreimer, D., Shuffling quantum field theory, Lett. Math. Phys. 51 (2000), no. 3, 179–191. 280Google Scholar
548. Krob, D., Leclerc, B., Thibon, J.-Y., Noncommutative symmetric functions. II. Transformations of alphabets, Internat. J. Algebra Comput. 7 (1997), no. 2, 181–264. 333Google Scholar
549. Krob, D. and Thibon, J.-Y., Noncommutative symmetric functions. IV. Quantum linear groups and Hecke algebras at q = 0, J. Algebraic Combin. 6 (1997), no. 4, 339–376. 333Google Scholar
550. Krob, D. and Thibon, J.-Y., Noncommutative symmetric functions. V. A degenerate version of Uq(glN), Internat. J. Algebra Comput. 9 (1999), no. 3-4, 405–430, Dedicated to the memory of Marcel-Paul Schützenberger. 333Google Scholar
551. Kung, J. P. S., A multiplication identity for characteristic polynomials of matroids, Adv. in Appl. Math. 32 (2004), no. 1-2, 319–326. 72Google Scholar
552. Kurosh, A. G., Lectures in general algebra, Translated by Ann Swinfen; translation edited by P. M. Cohn. International Series of Monographs in Pure and Applied Mathematics, Vol. 70, Pergamon Press, Oxford-Edinburgh-New York, 1965. 712Google Scholar
553. Lack, S., A 2-categories companion, Towards higher categories, IMA Vol. Math. Appl., vol. 152, Springer, New York, 2010, pp. 105–191. 760, 761Google Scholar
554. Lack, S. and Street, R., The formal theory of monads. II, J. Pure Appl. Algebra 175 (2002), no. 1-3, 243–265, Special volume celebrating the 70th birthday of Max Kelly. 760Google Scholar
555. Lack, S. and Street, R., A skew-duoidal Eckmann-Hilton argument and quantum categories, Appl. Categ. Structures 22 (2014), no. 5-6, 789–803. 133, 736Google Scholar
556. Lamarche, F., Exploring the gap between linear and classical logic, Theory Appl. Categ. 18 (2007), No. 17, 473–535, Running head paging: 471–533. 736Google Scholar
557. Lambe, L. A. and Radford, D. E., Introduction to the quantum Yang-Baxter equation and quantum groups: an algebraic approach, Mathematics and its Applications, vol. 423, Kluwer Academic Publishers, Dordrecht, 1997. 381, 526Google Scholar
558. Lambek, J., Deductive systems and categories. I. Syntactic calculus and residuated categories, Math. Systems Theory 2 (1968), 287–318. 736Google Scholar
559. Lambek, J., Éléments de mathématique, fascicule 22; Théorie des ensembles, Chapitre 4: Structures, by Nicolas Bourbaki. Hermann, Paris, 1966 . Deuxième édition, 108 pages., Canadian Mathematical Bulletin 11 (1968), no. 1, 155–156. 131Google Scholar
560. Lambek, J., Deductive systems and categories. II. Standard constructions and closed categories, Category Theory, Homology Theory and their Applications, I (Battelle Institute Conference, Seattle, Wash., 1968, Vol. One), Springer, Berlin, 1969, pp. 76–122. 203, 736Google Scholar
561. Lambek, J. and Scott, P. J., Introduction to higher order categorical logic, Cambridge Studies in Advanced Mathematics, vol. 7, Cambridge University Press, Cambridge, 1988, Reprint of the 1986 original. 493, 737, 760Google Scholar
562. Landers, R., Montgomery, S., Schauenburg, P., Hopf powers and orders for some bis-mash products, J. Pure Appl. Algebra 205 (2006), no. 1, 156–188. 468Google Scholar
563. Larson, R. G., Hopf algebras and group algebras, Ph.D. thesis, The University of Chicago, 1965. 233, 714, 715Google Scholar
564. Larson, R. G., Cocommutative Hopf algebras, Canad. J. Math. 19 (1967), 350–360. 233, 525, 714, 715Google Scholar
565. Larson, R. G., The order of the antipode of a Hopf algebra, Proc. Amer. Math. Soc. 21 (1969), 167–170. 525Google Scholar
566. Larson, R. G., Coseparable Hopf algebras, J. Pure Appl. Algebra 3 (1973), 261–267. 131Google Scholar
567. Larson, R. G. and Sweedler, M. E., An associative orthogonal bilinear form for Hopf algebras, Amer. J. Math. 91 (1969), 75–94. 525Google Scholar
568. Las Vergnas, M., Matroïdes orientables, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), Ai, A61–A64. 71Google Scholar
569. Las Vergnas, M., Convexity in oriented matroids, J. Combin. Theory Ser. B 29 (1980), no. 2, 231–243. 71Google Scholar
570. Lauve, A. and Mastnak, M., The primitives and antipode in the Hopf algebra of symmetric functions in noncommuting variables, Adv. in Appl. Math. 47 (2011), no. 3, 536–544. 333, 527Google Scholar
571. Lauve, A. and Mastnak, M., Bialgebra coverings and transfer of structure, Tensor categories and Hopf algebras, Contemp. Math., vol. 728, Amer. Math. Soc., Providence, RI, 2019, pp. 137– 153. 383Google Scholar
572. Lawvere, F. W., An elementary theory of the category of sets, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1506–1511. 736Google Scholar
573. Lawvere, F. W., An elementary theory of the category of sets, University of Chicago Lecture Notes, 1964. 736Google Scholar
574. Lawvere, F. W., More on graphic toposes, Cahiers Topologie Géom. Différentielle Catég. 32 (1991), no. 1, 5–10, International Category Theory Meeting (Bangor, 1989 and Cambridge, 1990). 493Google Scholar
575. Lawvere, F. W., Linearization of graphic toposes via Coxeter groups, J. Pure Appl. Algebra 168 (2002), no. 2-3, 425–436, Category theory 1999 (Coimbra). 493Google Scholar
576. Lawvere, F. W., Metric spaces, generalized logic, and closed categories [Rend. Sem. Mat. Fis. Milano 43 ( 1973 ), 135–166], Repr. Theory Appl. Categ. (2002), no. 1, 1–37, With an author commentary: Enriched categories in the logic of geometry and analysis. 494Google Scholar
577. Lawvere, F. W., An elementary theory of the category of sets (long version) with commentary, Repr. Theory Appl. Categ. (2005), no. 11, 1–35, Reprinted and expanded from Proc. Nat. Acad. Sci. U.S.A. 52 (1964), With comments by the author and Colin McLarty. 736Google Scholar
578. Lawvere, F. W. and Schanuel, S. H., Conceptual mathematics, second ed., Cambridge University Press, Cambridge, 2009, A first introduction to categories. 737Google Scholar
579. Lazard, M., Sur les algèbres enveloppantes universelles de certaines algèbres de Lie, C. R. Acad. Sci. Paris 234 (1952), 788–791. 712Google Scholar
580. Lazard, M., Sur les algèbres enveloppantes universelles de certaines algèbres de Lie, Publ. Sci. Univ. Alger. Sér. A. 1 (1954), 281–294 (1955). 712Google Scholar
581. Lazard, M., Lois de groupes et analyseurs, Ann. Sci. Ecole Norm. Sup. (3) 72 (1955), 299–400. 203Google Scholar
582. Lazard, M., Sur les groupes de Lie formels à un paramètre, Bull. Soc. Math. France 83 (1955), 251–274. 574Google Scholar
583. Lazard, M., Commutative formal groups, Lecture Notes in Mathematics, Vol. 443, Springer-Verlag, Berlin-New York, 1975. 574Google Scholar
584. Lazard, M., Lois de groupes et analyseurs, Séminaire Bourbaki, Vol. 3, Soc. Math. France, Paris, 1995, pp. Exp. No. 109, 77–91. 203Google Scholar
585. Le Bruyn, L., Noncommutative geometry and Cayley-smooth orders, Pure and Applied Mathematics, vol. 290, Chapman & Hall/CRC, Boca Raton, FL, 2008. 204Google Scholar
586. Lebed, V., Braided objects: Unifying algebraic structures and categorifying virtual braids, Ph.D. thesis, Université de Paris, 2012. 281Google Scholar
587. Lebed, V., Homologies of algebraic structures via braidings and quantum shuffles, J. Algebra 391 (2013), 152–192. 281Google Scholar
588. Leclerc, B., Dual canonical bases, quantum shuffles and q-characters, Math. Z. 246 (2004), no. 4, 691–732. 281Google Scholar
589. Lefschetz, S., Algebraic Topology, American Mathematical Society Colloquium Publications, v. 27, American Mathematical Society, New York, 1942. 571Google Scholar
590. Leinster, T., Higher operads, higher categories, London Mathematical Society Lecture Note Series, vol. 298, Cambridge University Press, Cambridge, 2004. 133, 203, 736, 760, 761Google Scholar
591. Leinster, T., Basic category theory, Cambridge Studies in Advanced Mathematics, vol. 143, Cambridge University Press, Cambridge, 2014. xivGoogle Scholar
592. Leinster, T., Basic bicategories, available at arXiv:math.CT/9810017. 760Google Scholar
593. Leĭtes, D. A., Lie superalgebras, Current problems in mathematics, Vol. 25, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1984, pp. 3–49. 673Google Scholar
594. Lemaire, J.-M., Algèbres connexes et homologie des espaces de lacets, Lecture Notes in Mathematics, Vol. 422, Springer-Verlag, Berlin-New York, 1974. 233Google Scholar
595. Leray, J., Sur la forme des espaces topologiques et sur les points fixes des représentations, J. Math. Pures Appl. (9) 24 (1945), 95–167. 127, 232, 233, 468, 526, 571, 573Google Scholar
596. Li, C. W. and Liu, X. Q., Algebraic structure of multiple stochastic integrals with respect to Brownian motions and Poisson processes, Stochastics Stochastics Rep. 61 (1997), no. 1-2, 107–120. 281, 676Google Scholar
597. Lin, J. P., H-spaces with finiteness conditions, Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 1095–1141. 572Google Scholar
598. Linchenko, V. V. and Montgomery, S., A Frobenius-Schur theorem for Hopf algebras, Algebr. Represent. Theory 3 (2000), no. 4, 347–355, Special issue dedicated to Klaus Roggenkamp on the occasion of his 60th birthday. 468Google Scholar
599. Linton, F. E. J., Autonomous categories and duality of functors, J. Algebra 2 (1965), 315–349. 761Google Scholar
600. Linton, F. E. J., Coequalizers in categories of algebras, Sem. on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Springer, Berlin, 1969, pp. 75–90. 761Google Scholar
601. Liu, Z., Norledge, W., Ocneanu, A., The adjoint braid arrangement as a combinatorial Lie algebra via the Steinmann relations, available at arXiv:1901.03243. 331Google Scholar
602. Livernet, M., From left modules to algebras over an operad: application to combinatorial Hopf algebras, Ann. Math. Blaise Pascal 17 (2010), no. 1, 47–96. 574Google Scholar
603. Livernet, M., Mesablishvili, B., Wisbauer, R., Generalised bialgebras and entwined monads and comonads, J. Pure Appl. Algebra 219 (2015), no. 8, 3263–3278. 167, 574, 761Google Scholar
604. Livernet, M. and Patras, F., Lie theory for Hopf operads, J. Algebra 319 (2008), no. 12, 4899–4920. 132, 716Google Scholar
605. Loday, J.-L., Série de Hausdorff, idempotents eulériens et algèbres de Hopf, Exposition. Math. 12 (1994), no. 2, 165–178. 278Google Scholar
606. Loday, J.-L., Cyclic homology, second ed., Grundlehren der Mathematischen Wissenschaften, vol. 301, Springer-Verlag, Berlin, 1998. 278, 440, 713, 714Google Scholar
607. Loday, J.-L., On the algebra of quasi-shuffles, Manuscripta Math. 123 (2007), no. 1, 79–93. 280Google Scholar
608. Loday, J.-L., Generalized bialgebras and triples of operads, Astérisque (2008), no. 320, x+116. 130, 279, 574, 714, 715, 716Google Scholar
609. Loday, J.-L. and Ronco, M. O., Algèbres de Hopf colibres, C. R. Math. Acad. Sci. Paris 337 (2003), no. 3, 153–158. 441Google Scholar
610. Loday, J.-L. and Ronco, M. O., On the structure of cofree Hopf algebras, J. Reine Angew. Math. 592 (2006), 123–155. 130, 279, 280, 441, 574Google Scholar
611. Loday, J.-L. and Vallette, B., Algebraic operads, Grundlehren der Mathematischen Wissenschaften, vol. 346, Springer, Heidelberg, 2012. 203, 204, 278, 279, 381, 383, 674Google Scholar
612. Lorenz, M., A tour of representation theory, Graduate Studies in Mathematics, vol. 193, American Mathematical Society, Providence, RI, 2018. 128, 129, 381, 383, 526, 713, 715Google Scholar
613. Lothaire, M., Combinatorics on words, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1997, With a foreword by Roger Lyndon and a preface by Dominique Perrin, Corrected reprint of the 1983 original, with a new preface by Perrin. 674, 675, 676, 713Google Scholar
614. Lukierski, J. and Rittenberg, V., Color-de Sitter and color-conformal superalgebras, Phys. Rev. D (3) 18 (1978), no. 2, 385–389. 673Google Scholar
615. Lundervold, A. and Munthe-Kaas, H., Backward error analysis and the substitution law for Lie group integrators, Found. Comput. Math. 13 (2013), no. 2, 161–186. 440Google Scholar
616. Lurie, J., Higher topos theory, Annals of Mathematics Studies, vol. 170, Princeton University Press, Princeton, NJ, 2009. 494, 737Google Scholar
617. Lyndon, R. C., On Burnside’s problem, Trans. Amer. Math. Soc. 77 (1954), 202–215. 278Google Scholar
618. Lyndon, R. C., A theorem of Friedrichs, Michigan Math. J. 3 (1955), 27–29. 674Google Scholar
619. Mac Lane, S., Cohomology theory of Abelian groups, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R. I., 1952, pp. 8–14. 278Google Scholar
620. Mac Lane, S., Natural associativity and commutativity, Rice Univ. Studies 49 (1963), no. 4, 28–46. 131, 735Google Scholar
621. Mac Lane, S., Categorical algebra, Bull. Amer. Math. Soc. 71 (1965), 40–106. 131, 203, 735, 736Google Scholar
622. Mac Lane, S., Homology, Classics in Mathematics, Springer-Verlag, Berlin, 1995, Reprint of the 1975 edition. 129, 278Google Scholar
623. Mac Lane, S., Categories for the working mathematician, second ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. 732, 736, 737, 760Google Scholar
624. Mac Lane, S. and Moerdijk, I., Sheaves in geometry and logic, Universitext, Springer-Verlag, New York, 1994. 737Google Scholar
625. Macdonald, I. G., Symmetric functions and Hall polynomials, second ed., The Clarendon Press Oxford University Press, New York, 1995, With contributions by A. Zelevinsky, Oxford Science Publications. 332Google Scholar
626. Magnus, W., Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935), no. 1, 259–280. 674Google Scholar
627. Magnus, W., Über Beziehungen zwischen höheren Kommutatoren, J. Reine Angew. Math. 177 (1937), 105–115. 674Google Scholar
628. Magnus, W., On the exponential solution of differential equations for a linear operator, Comm. Pure Appl. Math. 7 (1954), 649–673. 674Google Scholar
629. Magnus, W., Karrass, A., Solitar, D., Combinatorial group theory, second ed., Dover Publications, Inc., Mineola, NY, 2004, Presentations of groups in terms of generators and relations. 674Google Scholar
630. Majid, S., Algebras and Hopf algebras in braided categories, Advances in Hopf algebras (Chicago, IL, 1992), Lecture Notes in Pure and Appl. Math., vol. 158, Dekker, New York, 1994, pp. 55–105. 131, 677Google Scholar
631. Majid, S., Quantum and braided-Lie algebras, J. Geom. Phys. 13 (1994), no. 4, 307–356. 677Google Scholar
632. Majid, S., Foundations of quantum group theory, Cambridge University Press, Cambridge, 1995. 129, 130, 278, 383, 526, 675Google Scholar
633. Majid, S., A quantum groups primer, London Mathematical Society Lecture Note Series, vol. 292, Cambridge University Press, Cambridge, 2002. 131, 383Google Scholar
634. Malvenuto, C., Produits et coproduits des fonctions quasi-symétriques et de l’algèbre des descents, Ph.D. thesis, Laboratoire de combinatoire et d’informatique mathématique (LACIM), Univ. du Québec à Montréal, 1994. 333, 526, 636Google Scholar
635. Malvenuto, C. and Reutenauer, C., Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra 177 (1995), no. 3, 967–982. 526, 636Google Scholar
636. Manchon, D., L’algèbre de Hopf bitensorielle, Comm. Algebra 25 (1997), no. 5, 1537– 1551. 280, 526Google Scholar
637. Manchon, D., Hopf algebras in renormalisation, Handbook of algebra. Vol. 5, Elsevier/North-Holland, Amsterdam, 2008, pp. 365–427. 440, 525, 526Google Scholar
638. Manchon, D. and Paycha, S., Shuffle relations for regularised integrals of symbols, Comm. Math. Phys. 270 (2007), no. 1, 13–51. 333Google Scholar
639. Manchon, D. and Paycha, S., Nested sums of symbols and renormalized multiple zeta values, Int. Math. Res. Not. IMRN (2010), no. 24, 4628–4697. 280, 608Google Scholar
640. Manin, Y. I., Theory of commutative formal groups over fields of finite characteristic, Uspehi Mat. Nauk 18 (1963), no. 6 (114), 3–90. 128Google Scholar
641. Manin, Y. I., Some remarks on Koszul algebras and quantum groups, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 4, 191–205. 203Google Scholar
642. Manin, Y. I., Quantum groups and noncommutative geometry, Université de Montréal Centre de Recherches Mathématiques, Montreal, QC, 1988. 129, 203, 676Google Scholar
643. Manin, Y. I., Gauge field theory and complex geometry, second ed., Grundlehren der Mathematischen Wissenschaften, vol. 289, Springer-Verlag, Berlin, 1997, Translated from the 1984 Russian original by N. Koblitz and J. R. King. 130Google Scholar
644. Manin, Y. I., Introduction to the theory of schemes, Moscow Lectures, vol. 1, Springer, Cham, 2018, Translated from the Russian, edited and with a preface by Dimitry Leites. 128, 525Google Scholar
645. Manin, Y. I., Quantum groups and noncommutative geometry, second ed., CRM Short Courses, Centre de Recherches Mathématiques, [Montreal], QC; Springer, Cham, 2018. 129, 203, 676Google Scholar
646. Maranda, J.-M., Formal categories, Canadian J. Math. 17 (1965), 758–801. 736Google Scholar
647. Marberg, E., Strong forms of linearization for Hopf monoids in species, J. Algebraic Combin. 42 (2015), no. 2, 391–428. 132Google Scholar
648. Marberg, E., Strong forms of self-duality for Hopf monoids in species, Trans. Amer. Math. Soc. 368 (2016), no. 8, 5433–5473. 132Google Scholar
649. Marcinek, W., Generalized Lie algebras and related topics. I, II, Acta Univ. Wratislav. Mat. Fiz. Astronom. (1991), no. 55, 3–21, 23–52. 714Google Scholar
650. Marcolli, M., Feynman motives, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2010. 128Google Scholar
651. Margolis, S., Saliola, F. V., Steinberg, B., Combinatorial topology and the global dimension of algebras arising in combinatorics, J. Eur. Math. Soc. (JEMS) 17 (2015), no. 12, 3037–3080. 71Google Scholar
652. Margolis, S., Saliola, F. V., Steinberg, B., Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry, available at arXiv:1508.05446. 71Google Scholar
653. Markl, M., Operads and PROPs, Handbook of algebra. Vol. 5, Elsevier/North-Holland, Amsterdam, 2008, pp. 87–140. 203Google Scholar
654. Markl, M., Shnider, S., Stasheff, J. D., Operads in algebra, topology and physics, Mathematical Surveys and Monographs, vol. 96, American Mathematical Society, Providence, RI, 2002. 203Google Scholar
655. Mason, S. K., Recent trends in quasisymmetric functions, Recent trends in algebraic combinatorics, Assoc. Women Math. Ser., vol. 16, Springer, Cham, 2019, pp. 239–279. 333Google Scholar
656. Mastnak, M., On the cohomology of a smash product of Hopf algebras, available at arXiv:math/0210123. 382Google Scholar
657. Masuoka, A., The fundamental correspondences in super affine groups and super formal groups, J. Pure Appl. Algebra 202 (2005), no. 1-3, 284–312. 130Google Scholar
658. Masuoka, A., Formal groups and unipotent affine groups in non-categorical symmetry, J. Algebra 317 (2007), no. 1, 226–249. 574, 716Google Scholar
659. Masuoka, A., Hopf algebraic techniques applied to super algebraic groups, available at arXiv:1311.1261. 130Google Scholar
660. Masuoka, A. and Oka, T., Unipotent algebraic affine supergroups and nilpotent Lie superalgebras, Algebr. Represent. Theory 8 (2005), no. 3, 397–413. 715Google Scholar
661. May, J. P., Some remarks on the structure of Hopf algebras, Proc. Amer. Math. Soc. 23 (1969), 708–713. 572Google Scholar
662. May, J. P., The geometry of iterated loop spaces, Springer-Verlag, Berlin, 1972, Lectures Notes in Mathematics, Vol. 271. 203, 760Google Scholar
663. May, J. P. and Ponto, K., More concise algebraic topology, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2012, Localization, completion, and model categories. 129, 232, 233, 381, 572, 573, 714, 736Google Scholar
664. Mazurkiewicz, A., Concurrent program schemes and their interpretations, DAIMI Report Series 6 (1977), no. 78. 133Google Scholar
665. McCleary, J., A user’s guide to spectral sequences, second ed., Cambridge Studies in Advanced Mathematics, vol. 58, Cambridge University Press, Cambridge, 2001. 572Google Scholar
666. McConnell, J. C. and Robson, J. C., Noncommutative Noetherian rings, revised ed., Graduate Studies in Mathematics, vol. 30, American Mathematical Society, Providence, RI, 2001, With the cooperation of L. W. Small. 713Google Scholar
667. McCrudden, P., Categories of representations of coalgebroids, Adv. Math. 154 (2000), no. 2, 299–332. 736Google Scholar
668. McLarty, C., Elementary categories, elementary toposes, Oxford Logic Guides, vol. 21, The Clarendon Press, Oxford University Press, New York, 1992, Oxford Science Publications. 737Google Scholar
669. McMullen, P., Non-linear angle-sum relations for polyhedral cones and polytopes, Math. Proc. Cambridge Philos. Soc. 78 (1975), no. 2, 247–261. 72Google Scholar
670. McMullen, P. and Schulte, E., Abstract regular polytopes, Encyclopedia of Mathematics and its Applications, vol. 92, Cambridge University Press, Cambridge, 2002. 72Google Scholar
671. Meinrenken, E., Clifford algebras and Lie theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 58, Springer, Heidelberg, 2013. 713Google Scholar
672. Melançon, G. and Reutenauer, C., Lyndon words, free algebras and shuffles, Canad. J. Math. 41 (1989), no. 4, 577–591. 676Google Scholar
673. Méliot, P.-L., Representation theory of symmetric groups, Discrete Mathematics and its Applications, CRC Press, Boca Raton, FL, 2017. 129, 333, 526, 527, 636Google Scholar
674. Melliès, P.-A., Categorical semantics of linear logic, Interactive models of computation and program behavior, Panor. Synthèses, vol. 27, Soc. Math. France, Paris, 2009, pp. 1–196. 736, 737, 760Google Scholar
675. Méndez, M. A., Set operads in combinatorics and computer science, SpringerBriefs in Mathematics, Springer, Cham, 2015. 131, 132, 203, 282, 331, 383Google Scholar
676. Méndez, M. A. and Liendo, J. C., An antipode formula for the natural Hopf algebra of a set operad, Adv. in Appl. Math. 53 (2014), 112–140. 527Google Scholar
677. Menous, F., From dynamical systems to renormalization, J. Math. Phys. 54 (2013), no. 9, 092702, 24. 439, 440Google Scholar
678. Menous, F. and Patras, F., Logarithmic derivatives and generalized Dynkin operators, J. Algebraic Combin. 38 (2013), no. 4, 901–913. 440Google Scholar
679. Mesablishvili, B., Entwining structures in monoidal categories, J. Algebra 319 (2008), no. 6, 2496–2517. 761Google Scholar
680. Mesablishvili, B. and Wisbauer, R., Bimonads and Hopf monads on categories, J. K-Theory 7 (2011), no. 2, 349–388. 166, 167, 761Google Scholar
681. Mesablishvili, B. and Wisbauer, R., Notes on bimonads and Hopf monads, Theory Appl. Categ. 26 (2012), No. 10, 281–303. 167, 761Google Scholar
682. Meyer, D. M. and Smith, L., Poincaré duality algebras, Macaulay’s dual systems, and Steenrod operations, Cambridge Tracts in Mathematics, vol. 167, Cambridge University Press, Cambridge, 2005. 279Google Scholar
683. Meyer, P.-A., Quantum probability for probabilists, Lecture Notes in Mathematics, vol. 1538, Springer-Verlag, Berlin, 1993. 130Google Scholar
684. Michaelis, W., Lie coalgebras (with a proof of an analogue of the Poincaré-Birkhoff-Witt theorem), Ph.D. thesis, University of Washington, 1974. 675, 676, 715Google Scholar
685. Michaelis, W., Lie coalgebras, Adv. in Math. 38 (1980), no. 1, 1–54. 525, 675, 676, 715Google Scholar
686. Michaelis, W., The dual Poincaré-Birkhoff-Witt theorem, Adv. in Math. 57 (1985), no. 2, 93–162. 675, 715Google Scholar
687. Michaelis, W., The primitives of the continuous linear dual of a Hopf algebra as the dual Lie algebra of a Lie coalgebra, Lie algebra and related topics (Madison, WI, 1988), Contemp. Math., vol. 110, Amer. Math. Soc., Providence, RI, 1990, pp. 125–176. 674, 676Google Scholar
688. Michaelis, W., Coassociative coalgebras, Handbook of algebra, Vol. 3, Elsevier/North-Holland, Amsterdam, 2003, pp. 587–788. 129, 278, 279, 440, 526, 572, 675, 676, 715Google Scholar
689. Mielnik, B. and Plebański, J., Combinatorial approach to Baker-Campbell-Hausdorff exponents, Ann. Inst. H. Poincaré Sect. A (N.S.) 12 (1970), 215–254. 440, 712Google Scholar
690. Mikhalev, A. A., The Ado-Iwasawa theorem, graded Hopf algebras and residual finiteness of colored Lie (p-) superalgebras and their universal enveloping algebras, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1991), no. 5, 72–74. 130Google Scholar
691. Mikhalev, A. A., Shpilrain, V., Yu, J.-T., Combinatorial methods, CMS Books in Mathematics, vol. 19, Springer-Verlag, New York, 2004, Free groups, polynomials, and free algebras. 714Google Scholar
692. Mikhalev, A. A. and Zolotykh, A. A., Combinatorial aspects of Lie superalgebras, CRC Press, Boca Raton, FL, 1995. 673, 675, 714Google Scholar
693. Milne, J. S., Algebraic groups, Cambridge Studies in Advanced Mathematics, vol. 170, Cambridge University Press, Cambridge, 2017, The theory of group schemes of finite type over a field. 128, 525Google Scholar
694. Milnor, J. W., The Steenrod algebra and its dual, Ann. of Math. (2) 67 (1958), 150–171. 128Google Scholar
695. Milnor, J. W. and Moore, J. C., On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211–264. 127, 128, 232, 233, 234, 381, 525, 526, 572, 573, 671, 672, 673, 674, 675, 713, 714, 715Google Scholar
696. Milnor, J. W. and Moore, J. C., On the structure of Hopf algebras (preprint, 1959), Collected papers of John Milnor. V. Algebra, Edited by Hyman Bass and T. Y. Lam, American Mathematical Society, Providence, RI, 2010, pp. 7–36. 127, 128, 232, 233, 381, 525, 526, 572, 573, 672, 674, 713, 714, 715Google Scholar
697. Mimura, M. and Toda, H., Topology of Lie groups. I, II, Translations of Mathematical Monographs, vol. 91, American Mathematical Society, Providence, RI, 1991, Translated from the 1978 Japanese edition by the authors. 572Google Scholar
698. Minh, H. N., Structure of polyzetas and Lyndon words, Vietnam J. Math. 41 (2013), no. 4, 409–450. 280, 440, 608, 676, 713Google Scholar
699. Minh, H. N. and Petitot, M., Lyndon words, polylogarithms and the Riemann ζ function, Discrete Math. 217 (2000), no. 1-3, 273–292, Formal power series and algebraic combinatorics (Vienna, 1997). 676Google Scholar
700. Mitchell, B., Rings with several objects, Advances in Math. 8 (1972), 1–161. 204Google Scholar
701. Möbius, A. F., Über eine besondere Art von Umkehrung der Reihen, J. Reine Angew. Math. 9 (1832), 105–123. 71Google Scholar
702. Moerdijk, I., Monads on tensor categories, J. Pure Appl. Algebra 168 (2002), no. 2-3, 189–208, Category theory 1999 (Coimbra). 761Google Scholar
703. Montgomery, S. , Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, vol. 82, American Mathematical Society, Providence, RI, 1993. 129, 130, 131, 233, 332, 381, 383, 525, 526, 573, 673, 714, 715Google Scholar
704. Montgomery, S., Vega, M. D., Witherspoon, S., Hopf automorphisms and twisted extensions, J. Algebra Appl. 15 (2016), no. 6, 1650103, 14. 468Google Scholar
705. Moody, R. V. and Pianzola, A., Lie algebras with triangular decompositions, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1995, A Wiley-Interscience Publication. 713Google Scholar
706. Moore, J. C., Mimeographed notes of the algebraic topology seminar, Princeton, 1957– 1958. 127, 130, 233, 525, 526, 572, 573Google Scholar
707. Moore, J. C., Algèbres de Hopf universelles, Séminaire Henri Cartan; Volume 12. Exposé no. 10, Secrétariat mathématique, Paris, 1959–1960, pp. 1–11. 280, 281, 333Google Scholar
708. Moore, J. C., Compléments sur les algèbres de Hopf, Séminaire Henri Cartan; Volume 12. Exposé no. 4, Secrétariat mathématique, Paris, 1959–1960, pp. 1–12. 233, 573Google Scholar
709. Mosher, R. E. and Tangora, M. C., Cohomology operations and applications in homotopy theory, Harper & Row, Publishers, New York-London, 1968. 128Google Scholar
710. Moutard, T., Notes sur les équations aux dérivées partielles, J. de l’École Polytech-nique 64 (1894), 55–69. 381Google Scholar
711. Murfet, D., On Sweedler’s cofree cocommutative coalgebra, J. Pure Appl. Algebra 219 (2015), no. 12, 5289–5304. 281Google Scholar
712. Musson, I. M., Lie superalgebras and enveloping algebras, Graduate Studies in Mathematics, vol. 131, American Mathematical Society, Providence, RI, 2012. 675, 714Google Scholar
713. Neisendorfer, J., Lie algebras, coalgebras and rational homotopy theory for nilpotent spaces, Pacific J. Math. 74 (1978), no. 2, 429–460. 675Google Scholar
714. Neisendorfer, J., Algebraic methods in unstable homotopy theory, New Mathematical Monographs, vol. 12, Cambridge University Press, Cambridge, 2010. 714, 715Google Scholar
715. Neshveyev, S. and Tuset, L., Compact quantum groups and their representation categories, Cours Spécialisés, vol. 20, Société Mathématique de France, Paris, 2013. 129Google Scholar
716. Newman, K. W., Topics in the theory of irreducible Hopf algebras, Ph.D. thesis, Cornell University, 1970. 280, 281, 607Google Scholar
717. Newman, K. W., The structure of free irreducible, cocommutative Hopf algebras, J. Algebra 29 (1974), 1–26. 280, 607Google Scholar
718. Newman, K. W. and Radford, D. E., The cofree irreducible Hopf algebra on an algebra, Amer. J. Math. 101 (1979), no. 5, 1025–1045. 280, 281, 607Google Scholar
719. Nichols, W. D., Bialgebras, Ph.D. thesis, The University of Chicago, 1975. 234, 440, 572, 573, 675, 676, 714, 715Google Scholar
720. W. D. Pointed irreducible bialgebras, J. Algebra 57 (1979), no. 1, 64–76. 234, 278, 440, 572, 573, 574, 675, 676, 715Google Scholar
721. Nichols, W. D. and Sweedler, M. E., Hopf algebras and combinatorics, Umbral calculus and Hopf algebras (Norman, Okla., 1978), Contemp. Math., vol. 6, Amer. Math. Soc., Providence, RI, 1982, pp. 49–84. 129, 332Google Scholar
722. Nijenhuis, A. and Richardson, R. W., Jr., Cohomology and deformations of algebraic structures, Bull. Amer. Math. Soc. 70 (1964), 406–411. 672Google Scholar
723. Norledge, W. and Ocneanu, A., Hopf monoids, permutohedral tangent cones, and generalized retarded functions, available at arXiv:1911.11736. 331Google Scholar
724. Nouazé, Y. and Revoy, P., Un cas particulier du théorème de Poincaré-Birkhoff-Witt, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A329–A331. 712Google Scholar
725. Novelli, J.-C., Patras, F., Thibon, J.-Y., Natural endomorphisms of quasi-shuffle Hopf algebras, Bull. Soc. Math. France 141 (2013), no. 1, 107–130. 280, 712, 713Google Scholar
726. Onishchik, A. L. and Vinberg, E. B., Foundations of Lie theory, Lie groups and Lie algebras I, Encyclopaedia of Mathematical Sciences, vol. 20, Springer-Verlag, Berlin, 1993, Translated from the Russian by A. Kozlowski, pp. 1–94. 713Google Scholar
727. Orlik, P., Introduction to arrangements, CBMS Regional Conference Series in Mathematics, vol. 72, American Mathematical Society, Providence, RI, 1989. 72Google Scholar
728. Orlik, P., Lectures on arrangements: combinatorics and topology, Algebraic combinatorics, Universitext, Springer, Berlin, 2007, pp. 1–79. 72Google Scholar
729. Orlik, P. and Terao, H., Arrangements of hyperplanes, Grundlehren der Mathematischen Wissenschaften, vol. 300, Springer-Verlag, Berlin, 1992. 72Google Scholar
730. Oudom, J.-M., Coproduct and cogroups in the category of graded dual Leibniz algebras, Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995), Contemp. Math., vol. 202, Amer. Math. Soc., Providence, RI, 1997, pp. 115–135. 574Google Scholar
731. Oudom, J.-M., Théorème de Leray dans la catégorie des algèbres sur une opérade, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 2, 101–106. 574Google Scholar
732. Palmquist, P. H., The double category of adjoint squares, Reports of the Midwest Category Seminar, V (Zürich, 1970), Lecture Notes in Mathematics, Vol. 195, Springer, Berlin, 1971, pp. 123–153. 761Google Scholar
733. Pang, C. Y. A., Hopf algebras and Markov chains, Ph.D. thesis, Stanford University, 2014. 468Google Scholar
734. Pareigis, B., Non-additive ring and module theory. I. General theory of monoids, Publ. Math. Debrecen 24 (1977), no. 1-2, 189–204. 737Google Scholar
735. Pareigis, B., Non-additive ring and module theory. II. C-categories, C-functors and C-morphisms, Publ. Math. Debrecen 24 (1977), no. 3-4, 351–361. 736Google Scholar
736. Pareigis, B., A noncommutative noncocommutative Hopf algebra in “nature”, J. Algebra 70 (1981), no. 2, 356–374. 131Google Scholar
737. Pareigis, B., On Lie algebras in braided categories, Quantum groups and quantum spaces (Warsaw, 1995), Banach Center Publ., vol. 40, Polish Acad. Sci. Inst. Math., Warsaw, 1997, pp. 139–158. 677Google Scholar
738. Pareigis, B., On Lie algebras in the category of Yetter-Drinfeld modules, Appl. Categ. Structures 6 (1998), no. 2, 151–175. 677Google Scholar
739. Patras, F., Homothéties simpliciales, Ph.D. thesis, Université Paris 7, 1992. 572, 573, 714Google Scholar
740. Patras, F., La décomposition en poids des algèbres de Hopf, Ann. Inst. Fourier (Grenoble) 43 (1993), no. 4, 1067–1087. 278, 440, 468, 572, 714Google Scholar
741. Patras, F., L’algèbre des descentes d’une bigèbre graduée, J. Algebra 170 (1994), no. 2, 547–566. 468, 573, 714Google Scholar
742. Patras, F., A Leray theorem for the generalization to operads of Hopf algebras with divided powers, J. Algebra 218 (1999), no. 2, 528–542. 574Google Scholar
743. Patras, F., Dynkin operators and renormalization group actions in pQFT, Vertex operator algebras and related areas, Contemp. Math., vol. 497, Amer. Math. Soc., Providence, RI, 2009, pp. 169–184. 440Google Scholar
744. Patras, F. and Reutenauer, C., Higher Lie idempotents, J. Algebra 222 (1999), no. 1, 51–64. 573Google Scholar
745. Patras, F. and Reutenauer, C., Lie representations and an algebra containing Solomon’s, J. Algebraic Combin. 16 (2002), no. 3, 301–314 (2003). 382Google Scholar
746. Patras, F. and Reutenauer, C., On descent algebras and twisted bialgebras, Mosc. Math. J. 4 (2004), no. 1, 199–216, 311. 132, 332Google Scholar
747. Patras, F. and Schocker, M., Twisted descent algebras and the Solomon-Tits algebra, Adv. Math. 199 (2006), no. 1, 151–184. 132Google Scholar
748. Patras, F. and Schocker, M., Trees, set compositions and the twisted descent algebra, J. Algebraic Combin. 28 (2008), no. 1, 3–23. 132Google Scholar
749. Patrias, R., Antipode formulas for some combinatorial Hopf algebras, Electron. J. Combin. 23 (2016), no. 4, Paper 4.30, 32. 527Google Scholar
750. Petersen, T. K., Eulerian numbers, Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser/Springer, New York, 2015, With a foreword by Richard Stanley. 72Google Scholar
751. Poincaré, H., Sur les groupes continus, C. R. Acad. Sci. Paris 128 (1899), 1065–1069. 673, 711Google Scholar
752. Poincaré, H., Sur les groupes continus, Trans. Cambr. Philos. Soc. 18 (1900), 220–255. 673, 711Google Scholar
753. Poirier, S. and Reutenauer, C., Algèbres de Hopf de tableaux, Ann. Sci. Math. Québec 19 (1995), no. 1, 79–90. 636Google Scholar
754. Polishchuk, A. and Positselski, L., Quadratic algebras, University Lecture Series, vol. 37, American Mathematical Society, Providence, RI, 2005. 716Google Scholar
755. Porst, H.-E., Dual adjunctions between algebras and coalgebras, Arab. J. Sci. Eng. Sect. C Theme Issues 33 (2008), no. 2, 407–411. 383Google Scholar
756. Porst, H.-E., On categories of monoids, comonoids, and bimonoids, Quaest. Math. 31 (2008), no. 2, 127–139. 382Google Scholar
757. Porst, H.-E., Takeuchi’s free Hopf algebra construction revisited, J. Pure Appl. Algebra 216 (2012), no. 8-9, 1768–1774. 282Google Scholar
758. Porst, H.-E., The formal theory of Hopf algebras Part I: Hopf monoids in a monoidal category, Quaest. Math. 38 (2015), no. 5, 631–682. 131, 282Google Scholar
759. Porst, H.-E., The formal theory of Hopf algebras Part II: The case of Hopf algebras, Quaest. Math. 38 (2015), no. 5, 683–708. 282Google Scholar
760. Porst, H.-E., Hopf monoids in varieties, Algebra Universalis 79 (2018), no. 2, Art. 18, 28. 383Google Scholar
761. Postnikov, M., Lie groups and Lie algebras, “Mir”, Moscow, 1986, Lectures in geometry. Semester V, Translated from the Russian by Vladimir Shokurov. 713Google Scholar
762. Power, J., A unified approach to the lifting of adjoints, Cahiers Topologie Géom. Différentielle Catég. 29 (1988), no. 1, 67–77. 761Google Scholar
763. Power, J., 2-categories, BRICS Lecture Notes, Aarhus University NS-98-7 (1998). 760Google Scholar
764. Power, J. and Watanabe, H., Combining a monad and a comonad, Theoret. Comput. Sci. 280 (2002), no. 1-2, 137–162, Coalgebraic methods in computer science (Amsterdam, 1999). 761Google Scholar
765. Procesi, C., Lie groups, Universitext, Springer, New York, 2007, An approach through invariants and representations. 713Google Scholar
766. Quillen, D., Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205–295. 233, 279, 281, 439, 711, 712, 714Google Scholar
767. Quillen, D., Homotopy properties of the poset of nontrivial p-subgroups of a group, Adv. in Math. 28 (1978), no. 2, 101–128. 133Google Scholar
768. Quinn, D., The incidence algebra of posets and acyclic categories, Kyushu J. Math. 67 (2013), no. 1, 117–127. 204Google Scholar
769. Radford, D. E., Rationality and the theory of coalgebras, Ph.D. thesis, The University of North Carolina at Chapel Hill, 1970. 381Google Scholar
770. Radford, D. E., A natural ring basis for the shuffle algebra and an application to group schemes, J. Algebra 58 (1979), no. 2, 432–454. 278, 676Google Scholar
771. Radford, D. E., Hopf algebras, Series on Knots and Everything, vol. 49, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012. 129, 232, 233, 278, 280, 281, 282, 381, 383, 525, 526Google Scholar
772. Rains, E. M., The homology of real subspace arrangements, J. Topol. 3 (2010), no. 4, 786–818. 204Google Scholar
773. Ram, A., Quantum groups: a survey of definitions, motivations, and results, Geometric analysis and Lie theory in mathematics and physics, Austral. Math. Soc. Lect. Ser., vol. 11, Cambridge Univ. Press, Cambridge, 1998, pp. 20–104. 129Google Scholar
774. Ree, R., Lie elements and an algebra associated with shuffles, Ann. of Math. (2) 68 (1958), 210–220. 278, 439, 674Google Scholar
775. Ree, R., Generalized Lie elements, Canad. J. Math. 12 (1960), 493–502. 673, 674, 675Google Scholar
776. Reutenauer, C., Theorem of Poincaré-Birkhoff-Witt, logarithm and symmetric group representations of degrees equal to Stirling numbers, Combinatoire énumérative (Montreal, Que., 1985/Quebec, Que., 1985), Lecture Notes in Math., vol. 1234, Springer, Berlin, 1986, pp. 267–284. 440, 712Google Scholar
777. Reutenauer, C., Free Lie algebras, London Mathematical Society Monographs. New Series, vol. 7, The Clarendon Press, Oxford University Press, New York, 1993, Oxford Science Publications. 278, 333, 440, 526, 573, 674, 675, 676, 712, 713Google Scholar
778. Reutenauer, C., Free Lie algebras, Handbook of algebra, Vol. 3, Elsevier/North-Holland, Amsterdam, 2003, pp. 887–903. 674, 676Google Scholar
779. Rhodes, J. and Steinberg, B., The q-theory of finite semigroups, Springer Monographs in Mathematics, Springer, New York, 2009. 494Google Scholar
780. Riehl, E., Categorical homotopy theory, New Mathematical Monographs, vol. 24, Cambridge University Press, Cambridge, 2014. 730, 736, 737Google Scholar
781. Riehl, E., Category theory in context, Aurora, Dover Publications, 2016. xiv, 760Google Scholar
782. Rittenberg, V. and Wyler, D., Generalized superalgebras, Nuclear Phys. B 139 (1978), no. 3, 189–202. 673Google Scholar
783. Rittenberg, V. and Wyler, D., Sequences of Z2 ⊕ Z2 graded Lie algebras and superalgebras, J. Math. Phys. 19 (1978), no. 10, 2193–2200. 673Google Scholar
784. Rogers, A., Supermanifolds, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007, Theory and applications. 130Google Scholar
785. Roman, S., An introduction to the language of category theory, Compact Textbooks in Mathematics, Birkhäuser/Springer, Cham, 2017. xivGoogle Scholar
786. Rosas, M. H. and Sagan, B. E., Symmetric functions in noncommuting variables, Trans. Amer. Math. Soc. 358 (2006), no. 1, 215–232 (electronic). 333Google Scholar
787. Ross, L. E., On representations and cohomology of graded Lie algebras, Ph.D. thesis, University of California, Berkeley, 1964. 673, 713Google Scholar
788. Ross, L. E., Representations of graded Lie algebras, Trans. Amer. Math. Soc. 120 (1965), 17–23. 673, 713Google Scholar
789. Rosso, M., Groupes quantiques et algèbres de battage quantiques, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 2, 145–148. 281Google Scholar
790. Rosso, M., Integrals of vertex operators and quantum shuffles, Lett. Math. Phys. 41 (1997), no. 2, 161–168. 281Google Scholar
791. Rosso, M., Quantum groups and quantum shuffles, Invent. Math. 133 (1998), no. 2, 399–416. 281Google Scholar
792. Rota, G.-C., On the foundations of combinatorial theory. I. Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2 (1964), 340–368 (1964). 71Google Scholar
793. Saavedra Rivano, N., Catégories Tannakiennes, Lecture Notes in Mathematics, Vol. 265, Springer-Verlag, Berlin-New York, 1972. 131Google Scholar
794. Sagan, B. E., The symmetric group, second ed., Graduate Texts in Mathematics, vol. 203, Springer-Verlag, New York, 2001, Representations, combinatorial algorithms, and symmetric functions. 332Google Scholar
795. Saliola, F. V., The face semigroup algebra of a hyperplane arrangement, Canad. J. Math. 61 (2009), no. 4, 904–929. 71, 72, 204Google Scholar
796. Sam, S. V. and Snowden, A., Gröbner methods for representations of combinatorial categories, J. Amer. Math. Soc. 30 (2017), no. 1, 159–203. 132Google Scholar
797. Sam, S. V. and Snowden, A., Hilbert series for twisted commutative algebras, Algebr. Comb. 1 (2018), no. 1, 147–172. 132Google Scholar
798. Sam, S. V. and Snowden, A., Introduction to twisted commutative algebras, available at arXiv:1209.5122. 132, 381, 383Google Scholar
799. Samelson, H., Beiträge zur Topologie der Gruppen-Mannigfaltigkeiten, Ann. of Math. (2) 42 (1941), 1091–1137. 127, 232, 233, 571, 573Google Scholar
800. Samelson, H., Topology of Lie groups, Bull. Amer. Math. Soc. 58 (1952), 2–37. 571Google Scholar
801. Samelson, H., Heinz Hopf zum Gedenken. II. Zum wissenschaftlichen Werk von Heinz Hopf, Jber. Deutsch. Math.-Verein. 78 (1976/77), no. 3, 126–146. 572Google Scholar
802. Schauenburg, P., Duals and doubles of quantum groupoids (×R-Hopf algebras), New trends in Hopf algebra theory (La Falda, 1999), Contemp. Math., vol. 267, Amer. Math. Soc., Providence, RI, 2000, pp. 273–299. 737Google Scholar
803. Schauenburg, P., Actions of monoidal categories and generalized Hopf smash products, J. Algebra 270 (2003), no. 2, 521–563. 736Google Scholar
804. Scheunert, M., Generalized Lie algebras, J. Math. Phys. 20 (1979), no. 4, 712–720. 673, 714Google Scholar
805. Scheunert, M., The theory of Lie superalgebras, Lecture Notes in Mathematics, vol. 716, Springer, Berlin, 1979, An introduction. 130, 673, 713Google Scholar
806. Schlank, T. and Yanovski, L., The ∞–categorical Eckmann–Hilton argument, Algebr. Geom. Topol. 19 (2019), no. 6, 3119–3170. 133Google Scholar
807. Schlessinger, M. and Stasheff, J. D., The Lie algebra structure of tangent cohomology and deformation theory, J. Pure Appl. Algebra 38 (1985), no. 2-3, 313–322. 278, 675Google Scholar
808. Schmid, W., Poincaré and Lie groups, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 2, 175–186. 712Google Scholar
809. Schmitt, W. R., Antipodes and incidence coalgebras, Ph.D. thesis, Massachusetts Institute of Technology, 1986. 526Google Scholar
810. Schmitt, W. R., Antipodes and incidence coalgebras, J. Combin. Theory Ser. A 46 (1987), no. 2, 264–290. 526Google Scholar
811. Schmitt, W. R., Hopf algebras and identities in free partially commutative monoids, Theoret. Comput. Sci. 73 (1990), no. 3, 335–340. 133, 526Google Scholar
812. Schmitt, W. R., Hopf algebras of combinatorial structures, Canad. J. Math. 45 (1993), no. 2, 412–428. 133Google Scholar
813. Schmitt, W. R., Incidence Hopf algebras, J. Pure Appl. Algebra 96 (1994), no. 3, 299–330. 233, 332, 440, 525, 526, 712Google Scholar
814. Schneider, H.-J., Lectures on Hopf algebras, Trabajos de Matemática, vol. 31/95, Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, Córdoba, 1995, Notes by Sonia Natale. 129Google Scholar
815. Schocker, M., The module structure of the Solomon-Tits algebra of the symmetric group, J. Algebra 301 (2006), no. 2, 554–586. 71, 204Google Scholar
816. Schoeller, C., Γ−H-algèbres sur un corps, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), A655–A658. 572Google Scholar
817. Schubert, H., Categories, Springer-Verlag, New York-Heidelberg, 1972, Translated from the German by Eva Gray. 132, 760Google Scholar
818. Schur, J., Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen, J. Reine Angew. Math. 140 (1911), 1–28. 381Google Scholar
819. Schürmann, M., White noise on bialgebras, Lecture Notes in Mathematics, vol. 1544, Springer-Verlag, Berlin, 1993. 130, 381Google Scholar
820. Schützenberger, M. P., Sur une propriété combinatoire des algèbres de Lie libres pouvant être utilisée dans un problème de mathématiques appliquées., Séminaire Dubreil. Algèbre et théorie des nombres; Volume 12. Exposé no. 1, Secrétariat mathématique, Paris, 1958–1959, pp. 1–23. 278Google Scholar
821. Selick, P., Introduction to homotopy theory, Fields Institute Monographs, vol. 9, American Mathematical Society, Providence, RI, 1997. 128, 232, 233, 332, 525, 714Google Scholar
822. Serre, J.-P., Gèbres, Enseign. Math. (2) 39 (1993), no. 1-2, 33–85. 128, 525Google Scholar
823. Serre, J.-P., Lie algebras and Lie groups, Lecture Notes in Mathematics, vol. 1500, Springer-Verlag, Berlin, 2006, 1964 lectures given at Harvard University, Corrected fifth printing of the second (1992) edition. 440, 674, 675, 713, 714Google Scholar
824. Shepler, A. V. and Witherspoon, S., Poincaré-Birkhoff-Witt theorems, Commutative algebra and noncommutative algebraic geometry. Vol. I, Math. Sci. Res. Inst. Publ., vol. 67, Cambridge Univ. Press, New York, 2015, pp. 259–290. 716Google Scholar
825. Shnider, S. and Sternberg, S., Quantum groups, Graduate Texts in Mathematical Physics, II, International Press, Cambridge, MA, 1993, From coalgebras to Drinfeld algebras, A guided tour. 129, 278, 440, 468Google Scholar
826. Simpson, C., Homotopy theory of higher categories, New Mathematical Monographs, vol. 19, Cambridge University Press, Cambridge, 2012. 133, 737Google Scholar
827. Sinha, D. and Walter, B., Lie coalgebras and rational homotopy theory, I: graph coalgebras, Homology Homotopy Appl. 13 (2011), no. 2, 263–292. 675Google Scholar
828. Sinha, D. and Walter, B., Lie coalgebras and rational homotopy theory II: Hopf invariants, Trans. Amer. Math. Soc. 365 (2013), no. 2, 861–883. 675Google Scholar
829. Širšov, A. I., On the representation of Lie rings as associative rings, Uspehi Matem. Nauk (N.S.) 8 (1953), no. 5(57), 173–175. 712Google Scholar
830. Sjödin, G., Hopf algebras and derivations, J. Algebra 64 (1980), no. 1, 218–229. 572, 715Google Scholar
831. Sklyar, G. M. and Ignatovich, S. Y., Fliess series, a generalization of the Ree’s theorem, and an algebraic approach to a homogeneous approximation problem, Internat. J. Control 81 (2008), no. 3, 369–378. 676Google Scholar
832. Skowroński, A. and Yamagata, K., Frobenius algebras. I, EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2011, Basic representation theory. 129, 526Google Scholar
833. Smirnov, V. A., On the cochain complex of topological spaces, Mat. Sb. (N.S.) 115(157) (1981), no. 1, 146–158, 160. 203, 383Google Scholar
834. Smirnov, V. A., Simplicial and operad methods in algebraic topology, Translations of Mathematical Monographs, vol. 198, American Mathematical Society, Providence, RI, 2001, Translated from the Russian manuscript by G. L. Rybnikov. 203, 278, 675, 676, 714, 760Google Scholar
835. Smith, J. R., Cofree coalgebras over operads, Topology Appl. 133 (2003), no. 2, 105– 138. 281Google Scholar
836. Smoke, W. H., Differential operators on homogeneous spaces, Ph.D. thesis, University of California, Berkeley, 1965. 711, 712Google Scholar
837. Smoke, W. H., Invariant differential operators, Trans. Amer. Math. Soc. 127 (1967), 460– 494. 711, 712Google Scholar
838. Solomon, L., The Burnside algebra of a finite group, J. Combinatorial Theory 2 (1967), 603–615. 71Google Scholar
839. Solomon, L., On the Poincaré-Birkhoff-Witt theorem, J. Combinatorial Theory 4 (1968), 363–375. 712, 713Google Scholar
840. Sonner, J., Lifting inductive and projective limits, Canadian J. Math. 19 (1967), 1329– 1339. 131Google Scholar
841. Spanier, E. H., Algebraic topology, Springer-Verlag, New York-Berlin, 1981, Corrected reprint of the 1966 original. 572Google Scholar
842. Spivak, D. I., Category theory for the sciences, MIT Press, Cambridge, MA, 2014. 760Google Scholar
843. Stanley, R. P., Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, vol. 62, Cambridge University Press, Cambridge, 1999, With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin. 332, 333Google Scholar
844. Stanley, R. P., An introduction to hyperplane arrangements, Geometric combinatorics, IAS/Park City Math. Ser., vol. 13, Amer. Math. Soc., Providence, RI, 2007, pp. 389– 496. 72Google Scholar
845. Stanley, R. P., Enumerative combinatorics. Volume 1, second ed., Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 2012. 72, 381Google Scholar
846. Stasheff, J. D., Homotopy associativity of H-spaces. I, Trans. Amer. Math. Soc. 108 (1963), 275–292; II, 293–312. 203Google Scholar
847. Stasheff, J. D., H-spaces from a homotopy point of view, Lecture Notes in Mathematics, Vol. 161, Springer-Verlag, Berlin-New York, 1970. 279Google Scholar
848. Stasheff, J. D., Milnor’s work from the perspective of algebraic topology, Topological methods in modern mathematics (Stony Brook, NY, 1991), Publish or Perish, Houston, TX, 1993, pp. 5–22. 128Google Scholar
849. Steenrod, N. E., Cohomology operations, Lectures by N. E. Steenrod written and revised by D. B. A. Epstein. Annals of Mathematics Studies, No. 50, Princeton University Press, Princeton, NJ, 1962. 128, 525Google Scholar
850. Steinberg, B., Representation theory of finite monoids, Universitext, Springer, Cham, 2016. 72Google Scholar
851. Steiner, R., Decompositions of Hopf algebras, Bull. London Math. Soc. 14 (1982), no. 5, 392–396. 233, 573Google Scholar
852. Sthanumoorthy, N., Introduction to finite and infinite dimensional Lie (super)algebras, Elsevier/Academic Press, London, 2016. 714Google Scholar
853. Stolberg, H. J., Group cohomologies for Hopf algebras and other categories, Ph.D. thesis, Cornell University, 1969. 282Google Scholar
854. Stover, C. R., The equivalence of certain categories of twisted Lie and Hopf algebras over a commutative ring, J. Pure Appl. Algebra 86 (1993), no. 3, 289–326. 132, 574, 676, 715, 716Google Scholar
855. Straubing, H., Finite semigroup varieties of the form V ∗D, J. Pure Appl. Algebra 36 (1985), no. 1, 53–94. 494Google Scholar
856. Street, R., The formal theory of monads, J. Pure Appl. Algebra 2 (1972), no. 2, 149– 168. 760, 761Google Scholar
857. Street, R., Categorical structures, Handbook of algebra, Vol. 1, Elsevier/North-Holland, Amsterdam, 1996, pp. 529–577. 760Google Scholar
858. Street, R., Bicategory, Encyclopaedia of mathematics. Supplement. Vol. II (M. Hazewinkel, ed.), Kluwer Academic Publishers, Dordrecht, 2000, pp. 65– 67. 760Google Scholar
859. Street, R., Quantum groups, Australian Mathematical Society Lecture Series, vol. 19, Cambridge University Press, Cambridge, 2007, A path to current algebra. 129, 131, 204, 381, 526, 736, 737Google Scholar
860. Street, R., Monoidal categories in, and linking, geometry and algebra, Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 5, 769–821. 736Google Scholar
861. Strichartz, R. S., The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations, J. Funct. Anal. 72 (1987), no. 2, 320–345. 712Google Scholar
862. Strom, J., Modern classical homotopy theory, Graduate Studies in Mathematics, vol. 127, American Mathematical Society, Providence, RI, 2011. 133Google Scholar
863. Supina, M., The Hopf monoid of orbit polytopes, available at arXiv:1904.08437. 132Google Scholar
864. Sweedler, M. E., Cocommutative Hopf algebras with antipode, Ph.D. thesis, Massachusetts Institute of Technology, 1966. 233, 381, 525, 526, 672, 714, 715Google Scholar
865. Sweedler, M. E., Hopf algebras with one grouplike element, Trans. Amer. Math. Soc. 127 (1967), 515–526. 233, 573Google Scholar
866. Sweedler, M. E., The Hopf algebra of an algebra applied to field theory, J. Algebra 8 (1968), 262–276. 382Google Scholar
867. Sweedler, M. E., Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. xiii, xiv, 129, 130, 232, 233, 234, 278, 279, 281, 282, 381, 382, 383, 525, 526, 573, 672, 676, 714, 715Google Scholar
868. Switzer, R. M., Algebraic topology—homotopy and homology, Classics in Mathematics, Springer-Verlag, Berlin, 2002, Reprint of the 1975 original. 133Google Scholar
869. Szamuely, T., Galois groups and fundamental groups, Cambridge Studies in Advanced Mathematics, vol. 117, Cambridge University Press, Cambridge, 2009. 128Google Scholar
870. Taft, E. J., Witt and Virasoro algebras as Lie bialgebras, J. Pure Appl. Algebra 87 (1993), no. 3, 301–312. 675Google Scholar
871. Takeuchi, M., Free Hopf algebras generated by coalgebras, J. Math. Soc. Japan 23 (1971), 561–582. 282, 525Google Scholar
872. Takeuchi, M., Tangent coalgebras and hyperalgebras. I, Japan. J. Math. 42 (1974), 1–143. 128, 281Google Scholar
873. Takeuchi, M., Finite Hopf algebras in braided tensor categories, J. Pure Appl. Algebra 138 (1999), no. 1, 59–82. 131Google Scholar
874. Takeuchi, M., Survey of braided Hopf algebras, New trends in Hopf algebra theory (La Falda, 1999), Contemp. Math., vol. 267, Amer. Math. Soc., Providence, RI, 2000, pp. 301–323. 131Google Scholar
875. Takhtajan, L. A., Quantum mechanics for mathematicians, Graduate Studies in Mathematics, vol. 95, American Mathematical Society, Providence, RI, 2008. 130Google Scholar
876. Tamaroff, P., Cohomology of combinatorial species, Bachelor’s Thesis, Universidad de Buenos Aires, 2017. 132Google Scholar
877. Tate, J. and F. Oort, , Group schemes of prime order, Ann. Sci. École Norm. Sup. (4) 3 (1970), 1–21. 468Google Scholar
878. Terwilliger, P., Using Catalan words and a q-shuffle algebra to describe a PBW basis for the positive part of Uq(ŝl2), J. Algebra 525 (2019), 359–373. 281Google Scholar
879. Thibon, J.-Y., Lectures on noncommutative symmetric functions, Interaction of combinatorics and representation theory, MSJ Mem., vol. 11, Math. Soc. Japan, Tokyo, 2001, pp. 39–94. 333Google Scholar
880. Thibon, J.-Y. and Ung, B.-C.-V., Quantum quasi-symmetric functions and Hecke algebras, J. Phys. A 29 (1996), no. 22, 7337–7348. 636Google Scholar
881. Tilson, B., Categories as algebra: an essential ingredient in the theory of monoids, J. Pure Appl. Algebra 48 (1987), no. 1-2, 83–198. 494Google Scholar
882. Timmermann, T., An invitation to quantum groups and duality, EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2008, From Hopf algebras to multiplicative unitaries and beyond. 381, 526Google Scholar
883. Tits, J., Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. 71, 72Google Scholar
884. Tits, J., Two properties of Coxeter complexes, J. Algebra 41 (1976), no. 2, 265–268, Appendix to “A Mackey formula in the group ring of a Coxeter group” (J. Algebra 41 (1976), no. 2, 255–264) by Louis Solomon. 71Google Scholar
885. tom Dieck, T., Algebraic topology, EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2008. 129, 133Google Scholar
886. Ton-That, T. and Tran, T.-D., Poincaré’s proof of the so-called Birkhoff-Witt theorem, Rev. Histoire Math. 5 (1999), no. 2, 249–284 (2000). 712Google Scholar
887. Turaev, V. and Virelizier, A., Monoidal categories and topological field theory, Progress in Mathematics, vol. 322, Birkhäuser/Springer, Cham, 2017. 131, 761Google Scholar
888. Underwood, R. G., Fundamentals of Hopf algebras, Universitext, Springer, Cham, 2015. 129, 332Google Scholar
889. Vallette, B., Manin products, Koszul duality, Loday algebras and Deligne conjecture, J. Reine Angew. Math. 620 (2008), 105–164. 203, 736Google Scholar
890. van Lint, J. H. and Wilson, R. M., A course in combinatorics, second ed., Cambridge University Press, Cambridge, 2001. 334Google Scholar
891. van Osdol, D. H., Sheaves in regular categories, Exact categories and categories of sheaves, Lecture Notes in Math., vol. 236, Springer, Berlin, 1971, pp. 223–239. 761Google Scholar
892. van Osdol, D. H., Bicohomology theory, Trans. Amer. Math. Soc. 183 (1973), 449–476. 761Google Scholar
893. Varadarajan, V. S., Lie groups, Lie algebras, and their representations, Graduate Texts in Mathematics, vol. 102, Springer-Verlag, New York, 1984, Reprint of the 1974 edition. 713Google Scholar
894. Varadarajan, V. S., Supersymmetry for mathematicians: an introduction, Courant Lecture Notes in Mathematics, vol. 11, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2004. 714Google Scholar
895. Varchenko, A., Bilinear form of real configuration of hyperplanes, Adv. Math. 97 (1993), no. 1, 110–144. 71Google Scholar
896. Várilly, J. C., Hopf algebras in noncommutative geometry, Geometric and topological methods for quantum field theory (Villa de Leyva, 2001), World Sci. Publ., River Edge, NJ, 2003, pp. 1–85. 129Google Scholar
897. Vasilakopoulou, C., Generalization of algebraic operations via enrichment, Ph.D. thesis, University of Cambridge, 2014. 382, 383, 760Google Scholar
898. Vasilakopoulou, C., Enriched duality in double categories: V-categories and V-cocategories, J. Pure Appl. Algebra 223 (2019), no. 7, 2889–2947. 381, 382Google Scholar
899. Vasilakopoulou, C., Enrichment of categories of algebra and modules, available at arXiv:1205.6450. 382, 383Google Scholar
900. von Waldenfels, W., Zur Charakterisierung Liescher Elemente in freien Algebren, Arch. Math. (Basel) 17 (1966), 44–48. 675Google Scholar
901. Walters, R. F. C., The Eckmann–Hilton argument one dimension up, 1983, Report to the Sydney Category Seminar on a discussion of A. Carboni, F. W. Lawvere and R. F. C. Walters. 133Google Scholar
902. Ward, M., The algebra of lattice functions, Duke Math. J. 5 (1939), no. 2, 357–371. 71Google Scholar
903. Waterhouse, W. C., Introduction to affine group schemes, Graduate Texts in Mathematics, vol. 66, Springer-Verlag, New York-Berlin, 1979. 128Google Scholar
904. Webb, P., A guide to Mackey functors, Handbook of algebra, Vol. 2, Elsevier/North-Holland, Amsterdam, 2000, pp. 805–836. 133Google Scholar
905. Weibel, C. A., An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, Cambridge, 1994. 713Google Scholar
906. Weisner, L., Abstract theory of inversion of finite series, Trans. Amer. Math. Soc. 38 (1935), no. 3, 474–484. 71Google Scholar
907. White, J. A., Chromatic polynomials and rings in species, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), Discrete Math. Theor. Comput. Sci. Proc., AT, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2014, pp. 691–702. 132Google Scholar
908. White, J. A., Quasisymmetric functions from combinatorial Hopf monoids and Ehrhart theory, 2016, preprint. 132Google Scholar
909. Whitehead, G. W., Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. 525, 572Google Scholar
910. Wigner, D., An identity in the free Lie algebra, Proc. Amer. Math. Soc. 106 (1989), no. 3, 639–640. 675Google Scholar
911. Winter, D., The structure of fields, Springer-Verlag, New York-Heidelberg, 1974, Graduate Texts in Mathematics, No. 16. 715Google Scholar
912. Wisbauer, R., Algebras versus coalgebras, Appl. Categ. Structures 16 (2008), no. 1-2, 255–295. 167Google Scholar
913. Witt, E., Treue Darstellung Liescher Ringe, J. Reine Angew. Math. 177 (1937), 152– 160. 673, 674, 675, 711Google Scholar
914. Witt, E., Treue Darstellungen beliebiger Liescher Ringe, Collectanea Math. 6 (1953), 107–114. 711Google Scholar
915. Witt, E., Die Unterringe der freien Lieschen Ringe, Math. Z. 64 (1956), 195–216. 711Google Scholar
916. Wolf, M. C., Symmetric functions of non-commutative elements, Duke Math. J. 2 (1936), no. 4, 626–637. 333Google Scholar
917. Wolff, H., V -localizations and V -monads, J. Algebra 24 (1973), 405–438. 761Google Scholar
918. Wraith, G. C., Abelian Hopf algebras, J. Algebra 6 (1967), 135–156. 232, 573Google Scholar
919. Wraith, G. C., Hopf algebras over Hopf algebras, Ann. Mat. Pura Appl. (4) 76 (1967), 149– 163. 382Google Scholar
920. Yamamoto, S., Hoffman–Ihara operators and the formal power series operad, Proceedings of the 6th Workshop on Multiple Zeta, Kyushu Univ., Japan, 2013, In Japanese. 608Google Scholar
921. Yamamoto, S., Interpolation of multiple zeta and zeta-star values, J. Algebra 385 (2013), 102–114. 608Google Scholar
922. Yanagihara, H., Theory of Hopf algebras attached to group schemes, Lecture Notes in Mathematics, Vol. 614, Springer-Verlag, Berlin-New York, 1977. 128Google Scholar
923. Yau, D. and Johnson, M. W., A foundation for PROPs, algebras, and modules, Mathematical Surveys and Monographs, vol. 203, American Mathematical Society, Providence, RI, 2015. 203Google Scholar
924. Yetter, D. N., Functorial knot theory, Series on Knots and Everything, vol. 26, World Scientific Publishing Co., Inc., River Edge, NJ, 2001, Categories of tangles, coherence, categorical deformations, and topological invariants. 736Google Scholar
925. Yokonuma, T., Tensor spaces and exterior algebra, Translations of Mathematical Monographs, vol. 108, American Mathematical Society, Providence, RI, 1992, Translated from the 1977 Japanese edition by the author. 277Google Scholar
926. Zabrodsky, A., Hopf spaces, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1976, North-Holland Mathematics Studies, Vol. 22, Notas de Matemática, No. 59. 572Google Scholar
927. Zaslavsky, T., Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc. 1 (1975), no. issue 1, 154, vii+102. 71Google Scholar
928. Zassenhaus, H., A theorem of Friedrichs, Proc. and Trans. Roy. Soc. Canada, 3rd ser. 51 (1957), Section 3, 55–64. 674Google Scholar
929. Zelevinsky, A. V., Representations of finite classical groups, Lecture Notes in Mathematics, vol. 869, Springer-Verlag, Berlin, 1981, A Hopf algebra approach. 129, 332Google Scholar
930. Želobenko, D. P., Compact Lie groups and their representations, American Mathematical Society, Providence, RI, 1973, Translated from the Russian by Israel Program for Scientific Translations, Translations of Mathematical Monographs, Vol. 40. 713Google Scholar
931. Ziegler, G. M., Lectures on polytopes, Graduate Texts in Mathematics, vol. 152, Springer-Verlag, New York, 1995. 72Google Scholar
932. Zisman, M., Espaces de Hopf, algèbres de Hopf, Séminaire Henri Cartan; Volume 12. Exposé no. 2, Secrétariat mathématique, Paris, 1959–1960, pp. 1–17. 128, 232, 233, 572, 573Google Scholar

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