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A Categorical Axiomatics for Bisimulation
 In Proc. of CONCURâ€™98, LNCS 1466
, 1998
"... 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 2monads, T , on Cat. Operations on processes, such as nondeterministic sum, prefixing and parallel composition are modelled using functors in ..."
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Cited by 18 (8 self)
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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 2monads, T , on Cat. Operations on processes, such as nondeterministic sum, prefixing and parallel composition are modelled using functors in the Kleisli category for the 2monad T .
Pseudodistributive laws
, 2004
"... We address the question of how elegantly to combine a number of different structures, such as finite product structure, monoidal structure, and colimiting structure, on a category. Extending work of Marmolejo and Lack, we develop the definition of a pseudodistributive law between pseudomonads, and ..."
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Cited by 11 (0 self)
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We address the question of how elegantly to combine a number of different structures, such as finite product structure, monoidal structure, and colimiting structure, on a category. Extending work of Marmolejo and Lack, we develop the definition of a pseudodistributive law between pseudomonads, and we show how the definition and the main theorems about it may be used to model several such structures simultaneously. Specifically, we address the relationship between pseudodistributive laws and the lifting of one pseudomonad to the 2category of algebras and to the Kleisli bicategory of another. This, for instance, sheds light on the preservation of some structures but not others along the Yoneda embedding. Our leading examples are given by the use of open maps to model bisimulation and by the logic of bunched implications.
Talagrand's Inequality in Hereditary Settings
, 1998
"... We develop a nicely packaged form of Talagrand's inequality that can be applied to prove concentration of measure for functions de ned by hereditary properties. We illustrate the framework with several applications from combinatorics and algorithms. We also give an extension of the inequality v ..."
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Cited by 2 (0 self)
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We develop a nicely packaged form of Talagrand's inequality that can be applied to prove concentration of measure for functions de ned by hereditary properties. We illustrate the framework with several applications from combinatorics and algorithms. We also give an extension of the inequality valid in spaces satisfying a certain negative dependence property and give some applications.
Towards a Categorical Axiomatics of Bisimulation
, 1999
"... 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 2monads, T , on Cat. Operations on processes, such as nondeterministic sum, prefixing and parallel composition are modelled u ..."
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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 2monads, T , on Cat. Operations on processes, such as nondeterministic sum, prefixing and parallel composition are modelled using functors in the Kleisli category for the 2monad T . We may define the notion of open map for any such 2monad; 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 KZmonad, 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 KZmonad, 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...