We introduce the notion of <em>strong concatenable process</em> for Petri nets as the least refinement of non-sequential (concatenable) processes which can be expressed abstractly by means of a <em> functor</em> Q[_] from the category of Petri nets to an appropriate category of symmetric strict monoidal categories with free non-commutative monoids of objects, in the precise sense that, for each net N, the strong concatenable processes of N are isomorphic to the arrows of Q[N]. This yields an axiomatization of the causal behaviour of Petri nets in terms of symmetric strict monoidal categories.<br /> <br />In addition, we identify a <em>coreflection</em> right adjoint to Q[_] and we characterize its replete image in the category of symmetric monoidal categories, thus yielding an abstract description of the category of net computations.
Wiring diagrams as normal forms for computing in symmetric monoidal categories
