Strong Concatenable Processes: An Approach to the Category of Petri Net Computations

Abstract

We introduce the notion of strong concatenable process for Petri nets as the least refinement of non-sequential (concatenable) processes which can be expressed abstractly by means of a functor 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.

In addition, we identify a coreflection 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.