A pre-net is a Petri net equipped with an ordering on the input and output of each event. These give appropriate data from which to freely generate a strict monoidal category or a symmetric strict monoidal category, whereas a Petri net is appropriate data from which to freely generate a commutative monoidal category. Pre-nets are the same as the tensor schemes defined by Joyal and Street.
A pre-net is a pair of functions
where is the set of events, is the set of places, and is the free monoid on the set .
A morphism of of pre-nets is a pair of functions between the sets of events and places making the following diagrams commute
This defines a category of pre-nets and pre-net homomorphisms.
Pre-nets were introduced in
Tensor schemes were introduced in
Last revised on August 23, 2025 at 18:34:01. See the history of this page for a list of all contributions to it.