Adhesive and quasiadhesive categories

RAIRO - Theoretical Informatics and Applications

Volumn 39, Issue 3, 2005, Pages 511-545

  Lack, Stephen ^a   Sobociński, Pawel ^b  

^a UNIVERSITY OF WESTERN SYDNEY   (Australia)

^b AARHUS UNIVERSITY   (Denmark)

Author keywords

Adhesive categories; Category theory; Extensive categories; Graph rewriting; Quasiadhesive categories

Indexed keywords

COMPUTER GRAPHICS; COMPUTER SCIENCE; DISTRIBUTED COMPUTER SYSTEMS; GRAPH THEORY; MATHEMATICAL MODELS; SEMANTICS; THEOREM PROVING;

ADHESIVE CATEGORIES; CATEGORY THEORY; EXTENSIVE CATEGORIES; GRAPH REWRITING; QUASIADHESIVE CATEGORIES;

ADHESIVES;

EID: 22944475309     PISSN: 09883754     EISSN: 28047346     Source Type: Journal    
DOI: 10.1051/ita:2005028     Document Type: Conference Paper

References (24)

1. 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.
2. R. Brown and G. Janelidze, Van Kampen theorems for categories of covering morphisms in lextensive categories. J. Pure Appl. Algebra 119 (1997) 255-263.
3. A. Carboni, S. Lack and R.F.C. Walters, Introduction to extensive and distributive categories. J. Pure Appl. Algebra 84 (1993) 145-158.
4. L. Cardelli, Bitonal membrane systems. Draft (2003).
5. 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.
6. V. Danos and C. Laneve, Graphs for core molecular biology, in International Workshop on Computational Methods in Systems Biology, CMSB '03 (2003).
7. H. Ehrig, 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.
8. 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).
9. 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.
10. H. Ehrig, A. Habel, H.-J. Kreowski and F. Parisi-Presicce, 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.
11. 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).
12. H. Ehrig and B. König, 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.
13. 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).
14. H. Ehrig, M. Pfender and H.J. Schneider, Graph-grammars: an algebraic approach, in IEEE Conf. on Automata and Switching Theory (1973) 167-180.
15. F. Gadducci and U. Montanari, A concurrent graph semantics for mobile ambients, in Mathematical Foundations of Programming Semantics MFPS '01, ENTCS. Elsevier 45 (2001).
16. H.-J. Kreowski, Transformations of derivation sequences in graph grammars. Lect. Notes Comput. Sci. 56 (1977) 275-286.
17. S. Lack and P. Sobociński, Adhesive categories, in Proceedings of FOSSACS '04, Springer. Lect. Notes Comput. Sci. 2987 (2004) 273-288.
18. S. Lack and P. Sobociński, Quasitoposes, quasiadhesive categories and Artin glueing, in preparation (2005).
19. J. Lambek and P.J. Scott, Introduction to higher order categorical logic, Cambridge studies in advanced mathematics. Cambridge University Press 7 (1986).
20. R. Milner, Bigraphical reactive systems: Basic theory, Technical Report 523, Computer Laboratory, University of Cambridge (2001).
21. 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.
22. G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Tranformation, Volume 1: Foundations. World Scientific (1997).
23. V. Sassone and P. Sobociński, Deriving bisimulation congruences using 2-categories. Nordic J. Comput. 10 (2003) 163-183.
24. V. Sassone and P. Sobociński, Congruences for contextual graph-rewriting, Technical Report RS-04-11, BRICS, University of Aarhus (June 2004).