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.


A pre-net is a pair of functions

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

A morphism of of pre-nets (f:EE,g:PP)(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 PreNetPreNet of pre-nets and pre-net homomorphisms.


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.