Abstract

Abstract. We show that the generic symmetric monoidal category with a commutative separable algebra which has a Σ-family of actions is the category of cospans of finite Σ-labelled graphs restricted to finite sets as objects, thus providing a syntax for automata on the alphabet Σ. We use this result to produce semantic functors for Σautomata. 1. Introduction. A variety of authors have considered (bi-)categories of cospans (and spans) of graphs in the study of algebras of processes. The present authors have concentrated attention on algebras of automata (in [11] , [12], [13], [20], [23]), cospan operations providing the sequential operations, and span operations corresponding parallel operations. In another

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