Open maps, behavioural equivalences, and congruences

  • Allan Cheng
  • Mogens Nielsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1059)


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.


Open maps P-bisimilarity P-factorisability congruences process algebra category theory 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Allan Cheng
    • 1
  • Mogens Nielsen
    • 1
  1. 1.Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer ScienceNy Munkegade University of AarhusAarhusDenmark

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