A Categorical Semantics for Hierarchical Petri Nets

We show how a particular variety of hierarchical nets, where the firing of a transition in the parent net must correspond to an execution in some child net, can be modelled utilizing a functorial semantics from a free category – representing the parent net – to the category of sets and spans between them. This semantics can be internalized via Grothendieck construction, resulting in the category of executions of a Petri net representing the semantics of the overall hierarchical net. We conclude the paper by giving an engineering-oriented overview of how our model of hierarchical nets can be implemented in a transaction-based smart contract environment.