I will present a new formalism for Petri nets based on polynomial-style finite-set configurations and etale maps.  The processes of a Petri net P are etale maps G -> P from graphs.  The main feature of the formalism is that Petri nets have elements --- they are the elements you see in the pictures.  This makes the definition more representable (in the categorical sense of the word) than previous definitions.  The main result I want to arrive at is that P-processes form a symmetric monoidal Segal space, which is the free prop-in-groupoids on P, but most of the time will be spent just explaining Petri nets, their markings and firings, the token game, processes, and the basic idea of concurrency and causality -- and how these notions look in the new formalism.

Reference: "Elements of Petri nets and processes" [ArXiv:2005.05108]