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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 𝒬(_) 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 𝒬(N). In addition, we identify a coreflection right adjoint to 𝒬(_) and characterize its replete image, thus yielding an axiomatization of the category of net computations.