Generic commutative separable algebras and cospans of graphs

R. Rosebrugh, N. Sabadini and R.F.C. Walters

We show that the generic symmetric monoidal category with a commutative separable algebra which has a $\Sigma$-family of actions is the category of cospans of finite $\Sigma$-labelled graphs restricted to finite sets as objects, thus providing a syntax for automata on the alphabet $\Sigma$. We use this result to produce semantic functors for $\Sigma$-automata.

Keywords: separable algebra, cospan category

2000 MSC: 18B20, 18D10, 68Q05, 68Q85

Theory and Applications of Categories, Vol. 15, CT2004, No. 6, pp 164-177.

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