Concurrent Process Histories and Resource Transducers

TL;DR

This paper develops a categorical framework for understanding concurrent process histories and resource transducers, providing a graphical formalism and exploring their algebraic properties.

Contribution

It extends categorical theories of resource convertibility to model concurrent interactions and introduces categories of resource transducers with novel structures.

Findings

Formalism admits intuitive string diagram representation.

Categories of resource transducers have unique algebraic properties.

Framework captures the algebraic structure of concurrent process histories.

Abstract

We identify the algebraic structure of the material histories generated by concurrent processes. Specifically, we extend existing categorical theories of resource convertibility to capture concurrent interaction. Our formalism admits an intuitive graphical presentation via string diagrams for proarrow equipments. We also consider certain induced categories of resource transducers, which are of independent interest due to their unusual structure.