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**1 - 1**of**1**### On the Semantics of Message Passing Processes

, 1999

"... Let J be a shape in some category Shp for which there is a functor : Shp Cat. A categorical transition system (or system) is a pair (J; (J) C) consisting of a shape labelled by a functor in a category in C. Systems generalize conventional labelled transition systems. By choosing a suitable univer ..."

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Let J be a shape in some category Shp for which there is a functor : Shp Cat. A categorical transition system (or system) is a pair (J; (J) C) consisting of a shape labelled by a functor in a category in C. Systems generalize conventional labelled transition systems. By choosing a suitable universe of shapes, systems can model concurrent and asynchronous computation. By labelling in a category, rather than an alphabet or term algebra, the actions of an algorithm or process can have structure. We study a class of systems called twisted systems having the form S = (J; F e J C) where J is a reflexive graph and g (\Gamma) : RGrph RGrph is the twisted graph construction. The relevance of twisted systems lies in the relationship between twists and spans. A functor FJ Sp(C) into a bicategory of spans is equivalent to a functor F e J C. The connection with spans means that when the target category C = Set, then following Burstall, a twisted system can be viewed as a generalized flow-chart...