The concatenable processes of a Petri net N can be characterized ly as the arrows of a symmetric monoidal category P[N]. Yet, this is only a partial axiomatization, since P[N] is built on a concrete, ad hoc chosen, category of symmetries. In this paper we give a fully equational description of the category of concatenable processes of N, thus yielding an axiomatic theory of the noninterleaving behaviour of Petri nets.