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Quotients of groupoids by an action of a group

Published online by Cambridge University Press:  24 October 2008

John Taylor
John Taylor
Affiliation:
Department of Mathematics, University of the West Indies, Mona, Kingston 7, Jamaica, West Indies
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Extract

For any category A and group G there is a category AG of A-objects with G-action. An object of AG is an A-object A together with a group morphism, θA:G → Isom (A, A), of G into the group of invertible A-morphisms A → A. A morphism of AG is an A-morphism f: A → B which commutes with the G-action; that is, for each g∈G, the following diagram commutes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 239 - 249
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Armstrong, M. A.. On the fundamental group of an orbit space. Proc. Cambridge Philos. Soc. 61 (1965), 639–646.CrossRefGoogle Scholar
[2]Armstrong, M. A.. The fundamental group of the orbit space of a discontinuous group. Proc. Cambridge Philos. Soc. 64 (1968), 299–301.CrossRefGoogle Scholar
[3]Armstrong, M. A.. Calculating the fundamental group of an orbit space. Proc. Amer. Math. Soc. 84 (1982), 267–271.CrossRefGoogle Scholar
[4]Armstrong, M. A.. Lifting homotopies through fixed points. Proc. Roy. Soc. Edinburgh Sect. A 93 (1982), 123–128.Google Scholar
[5]Armstrong, M. A.. Lifting homotopies through fixed points II. Proc. Roy. Soc. Edinburgh Sect. A 96 (1984), 201–205.Google Scholar
[6]Brown, R.. Elements of Modern Topology (McGraw-Hill, 1968), 2nd Edition (Ellis Horwood, to appear).Google Scholar
[7]Brown, R.. Fibrations of groupoids. J. Algebra 15 (1970), 103–132.CrossRefGoogle Scholar
[8]Brown, R.. Groupoids as coefficients. Proc. London Math. Soc. (3) 25 (1972), 413–426.CrossRefGoogle Scholar
[9]Brown, R.. From groups to groupoids: a brief survey. Bull. London Math. Soc. 19 (1987), 113–134.CrossRefGoogle Scholar
[10]Brown, R. and Danesh-Naruie, G.. The fundamental groupoid as a topological groupoid. Proc. Edinburgh Math. Soc. 19 (1974), 237–244.CrossRefGoogle Scholar
[11]Brown, R. and Higgins, P. J.. On the fundamental groupoid of an orbit space. U.C.N.W. Preprint (1987).Google Scholar
[12]Ehresmann, C.. Oeuvres complètes et commentées. Ed. Andrée C. Ehresmann, Suppl. 1, 2.Cah. Top. Géom. Diff. 24 (1983) Parties 1–1, 1–2.Google Scholar
[13]Higgins, P. J.. Presentations of groupoids, with applications to groups. Proc. Cambridge Philos. Soc. 60 (1964), 7–20.CrossRefGoogle Scholar
[14]Higgins, P. J.. Categories and groupoids. Van Nostrand Mathematical Studies 32 (Van Nostrand, 1971).Google Scholar
[15]Higgins, P. J. and Taylor, J.. The fundamental groupoid and homotopy crossed complex of an orbit space. In Category Theory: Proceedings Gummersbach 1981, ed. Kamps, K. H. et al. , Lecture Notes in Math. vol. 962 (Springer-Verlag, 1982), pp. 115–122.CrossRefGoogle Scholar
[16]Mackey, G. W.. Ergodic theory and virtual groups. Math. Ann. 166 (1966), 187–207.CrossRefGoogle Scholar
[17]Salleh, A. Razak and Taylor, J.. On the relation between the fundamental groupoids of the classifying space and the nerve of an open cover. J. Pure Appl. Algebra 37 (1985), 81–93.CrossRefGoogle Scholar
[18]Rhodes, F.. On the fundamental group of a transformation group. Proc. London Math. Soc. (3) 16 (1966), 635–650.CrossRefGoogle Scholar
[19]Taylor, J.. Group actions on ω-groupoids and crossed complexes, and the homotopy groups of orbit spaces. Ph.D. thesis, University of Durham (1982).Google Scholar