Abstract:
Spans of open maps have been proposed by Joyal, Nielsen, and Winskel as a
way of adjoining an abstract equivalence, 
-bisimilarity, to a
category of models of computation 
, where 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 -bisimilarity. We address the following
fundamental question: given a category of models of computation and a category of observations , are there any conditions
under which algebraic constructs viewed as functors preserve -bisimilarity? We define the notion of functors being -factorisable, show how this ensures that -bisimilarity
is a congruence with respect to such functors. Guided by the definition
of -factorisability we show how it is possible to parametrise
proofs of functors being -factorisable with respect to the
category of observations , i.e., with respect to a behavioural
equivalence.
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