GENERIC COMMUTATIVE SEPARABLE ALGEBRAS AND COSPANS OF GRAPHS

We show that the generic symmetric monoidal category with a commu- tative 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 Σ- automata.

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