A taste of categorical Petri nets - Ermel, Claudia; Martini, Alfio (Techn. Univ. Berlin, Fachbereich 13, Informatik, 1996)
Abstract: "This report aims at providing introductory concepts for a categorical approach for the study of Petri Nets. After motivating why a categorical approach for studying petri nets might be desirable, we show that 'classical' place/transition Nets, usually seen as bipartite directed graphs, can be naturally given a monoid structure. Upon this idea we construct a category with place/transition Nets as objects and a suitable notion of place/transition Net morphisms as morphisms. We also verify the existence of ubiquitous categorical constructions in order to verify issues concerning cocompleteness. In the end, the usual notion of semantics of place/transition Nets by a marking graph construction is shown to be nothing else than an adjoint situation between two suitable functors. Further points of interest are pointed out in the bibliographic notes."
Keywords: Categories (Mathematics); Morphisms (Mathematics); Petri nets