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 a coreflection right adjoint to [Qscr ](_) and characterize its replete image, thus yielding an axiomatization of the category of net computations.