Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T03:12:04.026Z Has data issue: false hasContentIssue false
  • English
  • Français

Adhesive and quasiadhesive categories

Published online by Cambridge University Press:  15 July 2005

Stephen Lack  and
Paweł Sobociński
Stephen Lack
Affiliation:
School of Quantitative Methods and Mathematical Sciences, University of Western Sydney, Australia.
Paweł Sobociński
Affiliation:
BRICS, University of Aarhus, Denmark; pawel@brics.dk
Get access

Abstract

We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.

Keywords

Adhesive categoriesquasiadhesive categoriesextensive categoriescategory theorygraph rewriting
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 3: Foundations of Software Science and Computer Structures (FOSSECAS'04) , July 2005 , pp. 511 - 545
Copyright
© EDP Sciences, 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

P. Baldan, A. Corradini, H. Ehrig, M. Löwe, U. Montanari and F. Rossi, Concurrent semantics of algebraic graph transformations, in Handbook of Graph Grammars and Computing by Graph Transformation, edited by H. Ehrig, H.-J. Kreowski, U. Montanari and G. Rozenberg, World Scientific 3 (1999) 107–187.
Brown, R. and Janelidze, G., Van Kampen theorems for categories of covering morphisms in lextensive categories. J. Pure Appl. Algebra 119 (1997) 255–263. CrossRef
Carboni, A., Lack, S. and Walters, R.F.C., Introduction to extensive and distributive categories. J. Pure Appl. Algebra 84 (1993) 145–158. CrossRef
L. Cardelli, Bitonal membrane systems. Draft (2003).
A. Corradini, H. Ehrig, R. Heckel, M. Lowe, U. Montanari and F. Rossi, Algebraic approaches to graph transformation part i: Basic concepts and double pushout approach, in Handbook of Graph Grammars and Computing by Graph Transformation, edited by G. Rozenberg, World Scientific 1 (1997) 162–245.
V. Danos and C. Laneve, Graphs for core molecular biology, in International Workshop on Computational Methods in Systems Biology, CMSB '03 (2003).
Ehrig, H., Introduction to the algebraic theory of graph grammars, in 1st Int. Workshop on Graph Grammars, Springer Verlag. Lect. Notes Comput. Sci. 73 (1979) 1–69. CrossRef
H. Ehrig, G. Engels, H.-J. Kreowski and G. Rozenberg, editors, Handbook of Graph Grammars and Computing by Graph Transformation, Volume 2: Applications, Languages and Tools. World Scientific (1999).
H. Ehrig, M. Gajewsky and F. Parisi-Presicce, High-level replacement systems with applications to algebraic specificaitons and Petri Nets, in Handbook of Graph Grammars and Computing by Graph Transformation, edited by H. Ehrig, H.-J. Kreowsky, U. Montanari and G. Rozenberg, World Scientific 3 (1999) 341–400.
Ehrig, H., Habel, A., Kreowski, H.-J. and Parisi-Presicce, F., From graph grammars to high level replacement systems, in 4th Int. Workshop on Graph Grammars and their Application to Computer Science, Springer-Verlag. Lect. Notes Comp. Sci. 532 (1991) 269–291. CrossRef
H. Ehrig, A. Habel, H.-J. Kreowski and F. Parisi-Presicce, Parallelism and concurrency in high-level replacement systems. Math. Struct. Comp. Sci. 1 (1991).
Ehrig, H. and König, B., Deriving bisimulation congruences in the dpo approach to graph rewriting, in Foundations of Software Science and Computation Structures FoSSaCS '04, Springer. Lect. Notes Comput. Sci. 2987 (2004) 151–166. CrossRef
H. Ehrig, H.-J. Kreowski, U. Montanari and G. Rozenberg, editors, Handbook of Graph Grammars and Computing by Graph Transformation, Volume 3: Concurrency, Parallelism and Distribution. World Scientific (1999).
H. Ehrig, M. Pfender and H.J. Schneider, Graph-grammars: an algebraic approach, in IEEE Conf. on Automata and Switching Theory (1973) 167–180.
F. Gadducci and U. Montanari, A concurrent graph semantics for mobile ambients, in Mathematical Foundations of Programming Semantics MFPS '01, ENTCS. Elsevier 45 (2001).
Kreowski, H.-J., Transformations of derivation sequences in graph grammars. Lect. Notes Comput. Sci. 56 (1977) 275–286. CrossRef
Lack, S. and Sobociński, P., Adhesive categories, in Proceedings of FOSSACS '04, Springer. Lect. Notes Comput. Sci. 2987 (2004) 273–288. CrossRef
S. Lack and P. Sobociński, Quasitoposes, quasiadhesive categories and Artin glueing, in preparation (2005).
J. Lambek and P.J. Scott, Introduction to higher order categorical logic, Cambridge studies in advanced mathematics. Cambridge University Press 7 (1986).
R. Milner, Bigraphical reactive systems: Basic theory, Technical Report 523, Computer Laboratory, University of Cambridge (2001).
U. Montanari, M. Pistore and F. Rossi, Modelling concurrent, mobile and coordinated systems via graph transformations, in Handbook of Graph Grammars and Computing by Graph Transformation, edited by H. Ehrig, H.-J. Kreowski, U. Montanari and G. Rozenberg, World Scientific 3 (1999) 189–268.
G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Tranformation, Volume 1: Foundations. World Scientific (1997).
Sassone, V. and Sobociński, P., Deriving bisimulation congruences using 2-categories. Nordic J. Comput. 10 (2003) 163–183.
V. Sassone and P. Sobociński, Congruences for contextual graph-rewriting, Technical Report RS-04-11, BRICS, University of Aarhus (June 2004).