A Categorical Semantics for Hierarchical Petri Nets
Fabrizio Genovese, Jelle Herold
We show how a particular flavor 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 hiearchic nets can be
implemented in a transaction-based smart contract environment.