Relating Reversible Petri Nets and Reversible Event Structures, categorically

Petri nets, where causal dependencies are modelled via inhibitor arcs, called \emph{Causal nets}, are powerful enough to play the role of occurrence nets when representing the behaviour of a concurrent and distributed system, even when reversibility is considered. In this paper we extend Causal nets to account also for asymmetric conflicts and study (i) how these kind of nets, and their reversible versions, can be turned into a category; and (ii) their relation with the categories of reversible asymmetric event structures.