We introduce the notion of strongly concatenable process as a refinement of concatenable processes (Degano et al. 1996), which can be expressed axiomatically via a functor [Qscr](_) from the category of Petri nets to an appropriate category of symmetric strict monoidal categories, in the precise sense that, for each net N, the strongly concatenable processes of N are isomorphic to the arrows of [Qscr](N). In addition, we identify acoreflection right adjoint to [Qscr](_) and characterize its replete image, thus yielding an axiomatization of the category of net computations.