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Abstract: We give an axiomatic category theoretic account of bisimulation in process algebras based on the idea of functional bisimulations as open maps. We work with 2-monads, T , on Cat. Operations on processes, such as nondeterministic sum, prefixing and parallel composition are modelled using functors in the Kleisli category for the 2-monad T . (Update)
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.... as a model of nondeterministic processes which supports a notion of bisimulation and as well extends to higher order [7, 12, 5, 4, 3, 10, 13, 6, 2]. At the start of this work, the paper [7] showed that the category of (labelled) event structures embedded fully and...
...colimits by a functor between presheaf categories is sufficient to ensure that it preserves open maps and bisimulation. Proposition 2. 3 [8] Let G : Q be any connected colimit preserving functor between presheaf categories. Then G preserves open maps and open map bisimulation....
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BibTeX entry: (Update)
G. L. Cattani, A.J. Power, and G. Winskel, A categorical axiomatics for bisimulation, In Proceedings of CONCUR '98, Lecture Notes in Computer Science 1466 (1998) 581-596. http://citeseer.ist.psu.edu/cattani98categorical.html More
@inproceedings{ cattani98categorical,
author = "Gian Luca Cattani and John Power and Glynn Winskel",
title = "A Categorical Axiomatics for Bisimulation",
booktitle = "International Conference on Concurrency Theory",
pages = "581-596",
year = "1998",
url = "citeseer.ist.psu.edu/cattani98categorical.html" }
Citations (may not include all citations):1933 Communication and concurrency (context) - Milner - 1989
562 Categories for the working mathematician (context) - Lane - 1971
156 Basic concepts of enriched category theory (context) - Kelly - 1982
150 The category-theoretic solution of recursive domain equation.. (context) - Smyth, Plotkin - 1982
109 Continuous lattices (context) - Scott - 1972
80 Handbook of Categorical Algebra (context) - Borceux - 1994
80 Review of the elements of 2-categories (context) - Kelly, Street
69 Triples and Theories (context) - Barr, Wells - 1985
69 Information and Computation (context) - Joyal, Nielsen et al. - 1996
58 Presheaf Models for Concurrency - Cattani, Winskel - 1997
35 Monads for which structures are adjoint to units (context) - Kock - 1995
35 Two-dimensional monad theory (context) - Blackwell, Kelly et al. - 1989
34 Bisimulation for higher-order process calculi - Sangiorgi - 1996
33 A completeness theorem for open maps (context) - Joyal, Moerdijk - 1994
27 A presheaf semantics of value-passing processes - Winskel
21 A Theory of Recursive Domains with Applications to Concurren.. - Cattani, Fiore et al. - 1998
17 Presheaf Models for the - Calculus - Cattani, Stark et al. - 1997
9 Closed categories generated by commutative monads (context) - Kock - 1971
4 EACTS Bulletin (context) - Jacobs, Rutten et al. - 1997
4 On bisimulation for higher order processes (context) - Cattani, Winskel - 1998
4 Cahiers de Topologie et Geometrie Di erentielle (context) - Street, Bicategories - 1980
3 A representation result for free cocompletions - Power, Cattani et al.
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