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.

• 18M05 - Monoidal categories, symmetric monoidal categories
• 68-XX - Computer science
• 68Q85 - Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)