文章基本信息

标题：A Categorical Axiomatics for Bisimulation
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作者：Gian Luca Cattani ; John Power ; Glynn Winskel 等
期刊名称：BRICS Report Series
印刷版ISSN：0909-0878
出版年度：1998
卷号：5
期号：22
出版社：Aarhus University
摘要：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, prexing and parallel composition are modelled using functors in the Kleisli category for the 2-monad T. We may define the notion of open map for any such 2-monad; in examples of interest, that agrees exactly with the usual notion of functional bisimulation. Under a condition on T, namely that it be a dense KZ-monad, which we define, it follows that functors in Kl(T) preserve open maps, i.e., they respect functional bisimulation. We further investigate structures on Kl(T) that exist for axiomatic reasons, primarily because T is a dense KZ-monad, and we study how those structures help to model operations on processes. We outline how this analysis gives ideas for modelling higher order processes. We conclude by making comparison with the use of presheaves and profunctors to model process calculi.