Whole-grain Petri Nets and Processes

We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The supports both geometric semantics in the style of Goltz Reisig (processes are maps from graphs) an algebraic Meseguer Montanari, terms free coloured props, allows following unification: P net, Segal space P-processes is shown to be prop-in-groupoids P. There also unfolding \`a la Winskel, which bypasses classical symmetry problems: with new formalism, every net admits universal unfolding, turn has associated event structure Scott domain. Since everything encoded explicit sets, their processes have elements. In particular, individual-token native. (Collective-token emerges rather drastic quotient constructions Best-Devillers, involving taking {\pi}_0 groupoids states.)