Affiliations: Institute of Computer Science, Gdańsk Branch, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland. email: {m.bednarczyk,a.borzyszkowski}@ipipan.gda.pl | Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland. email: rsomla@univ.gda.pl
Note: [] Address for correspondence: Institute of Computer Science, Gdańsk Branch, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland
Note: [] Address for correspondence: Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland
Abstract: The problem of finite completeness of categories of Petri nets is studied. Since Petri nets have finite products, the problem reduces to the issue of the existence of equalizers. We show that the categories of Petri nets with general and Winskel morphisms do not admit equalizers, and hence are not finitely complete. The main positive result of the paper states that reachable Petri nets with multiplicative morphisms form a finitely complete category. As an application of this result, some well-known categories are shown to be finitely complete. For instance, since all morphisms between reachable safe Petri nets are multiplicative, it follows that the category of reachable safe Petri nets is finitely complete.
Keywords: Categories of Petri nets, products, equalizers, (finite) completeness
