String Diagrams for Physical Duoidal Categories

TL;DR

This paper introduces a graphical string diagram framework for physical duoidal categories, enabling clearer visualization and reasoning within this mathematical structure.

Contribution

It presents a novel string diagram formalism tailored for physical duoidal categories, enhancing understanding and manipulation of their morphisms.

Findings

String diagrams are adapted for physical duoidal categories.

Wires form a zigzag-free partial order in diagrams.

Nodes preserve order with interval inputs and outputs.

Abstract

We introduce string diagrams for physical duoidal categories (normal $\otimes$-symmetric duoidal categories): they consist of string diagrams with wires forming a zigzag-free partial order and order-preserving nodes whose inputs and outputs form intervals.