Spans of open maps have been proposed by Joyal, Nielsen, and Winskel as a way of adjoining an abstract equivalence, P-bisimilarity, to a category of models of computation M, where P is an arbitrary sub-category of observations. Part of the motivation was to recast and generalise Milner's well-known strong bisimulation in this categorical setting. An issue left open was the congruence properties of P-bisimilarity. We address the following fundamental question: given a category of models of computation M and a category of observations P, are there any conditions under which algebraic constructs viewed as functors preserve P-bisimilarity? We define the notion of functors being P -factorisable, show how this ensures that P-bisimilarity is a congruence with respect to such functors. Guided by the definition of P-factorisability we show how it is possible to parametrise proofs of functors being P-factorisable with respect to the category of observations P, i.e., with respect to a behavioural equivalence.
Lecture Notes in Computer Science: 21st International Colloquium Linköping, Sweden, April 22-24, 1996 Proceedings, 1996, p. 257-271
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Lecture Notes in Computer Science
International Colloquium on Trees in Algebra and Programming, 1996