In an attempt to understand the relationships and differences between the extensive amount of research within the field of bisimulation equivalences, Joyal, Nielsen, and Winskel recently proposed an abstract category-theoretic definition of bisimulation. They identify spans of morphisms satisfying certain "path lifting" properties, so-called open maps, as an abstract definition of bisimilarity. Furthermore, it was shown how to capture Milner's bisimulation and a variant of history-preserving bisimulations for event structures. In this paper we review the theory of open maps and show that the theory, in fact, captures not only bisimulations but many other behavioural equivalences. We also briefly present presheaf models as an abstract model of computation.
Lecture Notes in Computer Science: 15th Conference Bangalore, India, December 18-20, 1995 Proceedings, 1995, p. 263-278
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Lecture Notes in Computer Science
Foundations of Software Technology and Theoretical Computer Science Conference, 1995