An Axiomatization of the Algebra of Petri Net Concatenable Processes

The concatenable processes of a Petri net N can be characterized abstractly as the arrows of a symmetric monoidal category ~(N). However, this is only a partial axiomatization, since it is based on a concrete, ad hoe chosen, category of symmetries Sym N. In this paper we give a completely abstract characterization of the category of concatenable processes of N, thus yielding an axiomatic theory of the noninterleaving behaviour of Petri nets.