Open AccessA Categorical Axiomatics for Bisimulation
Author(s) -
Gian Luca Cattani,
John Power,
Glynn Winskel
Publication year - 1998
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v5i22.19428
Subject(s) - bisimulation , monad (category theory) , functor , nondeterministic algorithm , mathematics , axiom , process calculus , pure mathematics , category theory , model category , algebra over a field , discrete mathematics , computer science , theoretical computer science , geometry , homotopy , homotopy category
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.