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 subcategory 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 funetors being P-factorisable, show how this ensures that P-bisimitarity 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.
CITATION STYLE
Cheng, A., & Nielsen, M. (1996). Open maps, behavioural equivalences, and congruences. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1059, pp. 257–271). Springer Verlag. https://doi.org/10.1007/3-540-61064-2_42
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