Strong Concatenable Processes:
An Approach to the Category of
Petri Net Computations

Vladimiro Sassone

October 1994


We introduce the notion of strong concatenable process for Petri nets as the least refinement of non-sequential (concatenable) processes which can be expressed abstractly by means of a functor tex2html_wrap_inline26 from the category of Petri nets to an appropriate category of symmetric strict monoidal categories with free non-commutative monoids of objects, in the precise sense that, for each net N, the strong concatenable processes of N are isomorphic to the arrows of tex2html_wrap_inline32. This yields an axiomatization of the causal behaviour of Petri nets in terms of symmetric strict monoidal categories.

In addition, we identify a coreflection right adjoint to tex2html_wrap_inline26 and we characterize its replete image in the category of symmetric monoidal categories, thus yielding an abstract description of the category of net computations

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