## Towards a Categorical Axiomatics of Bisimulation (1999)

### BibTeX

@MISC{Cattani99towardsa,

author = {Gian Luca Cattani and A. John Power and Glynn Winskel},

title = {Towards a Categorical Axiomatics of Bisimulation},

year = {1999}

}

### OpenURL

### Abstract

We give an axiomatic category theoretic account of bisimulation in process algebras based on the idea of functional bisimulations as open maps. The axiomatisation centres on 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 . We may define the notion of open map for any such 2-monad; in examples of interest, the definition 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 compariso...