Pre-nets, read arcs and unfolding:
a functorial presentation

Pre-nets have been recently proposed as a means of providing a functorial algebraic semantics to Petri nets (possibly with read arcs), overcoming some previously unsolved subtleties of the classical model. Here we develop a functorial semantics for pre-nets following a sibling classical approach based on an unfolding construction. Any pre-net is mapped to an acyclic branching net, representing its behaviour, then to a prime event structure and finally to a finitary prime algebraic domain. Then the algebraic and unfolding view are reconciled: we exploit the algebraic semantics to define a functor from the category of pre-nets to the category of domains that is shown to be naturally isomorphic to the unfolding-based functor. All the results are extended to pre-nets with read arcs.