# nLab pre-net

## Idea

A pre-net is a Petri net equipped with an ordering on the input and output of each event. These freely generate strict symmetric monoidal categories whereas Petri nets freely generate commutative monoidal categories. Pre-nets are the same as the tensor schemes defined by Joyal and Street.

## Definition

A pre-net is a pair of functions

where $E$ is the set of events, $P$ is the set of places, and $P^*$ is the free monoid on the set $P$.

A morphism of of pre-nets $(f \colon E \to E', g \colon P \to P')$ is a pair of functions between the sets of events and places making the following diagrams commute

This defines a category $PreNet$ of pre-nets and pre-net homomorphisms.

## References

Pre-nets were introduced in

Tensor schemes were introduced in

Last revised on December 1, 2019 at 12:44:42. See the history of this page for a list of all contributions to it.