String Diagrams for Closed Symmetric Monoidal Categories
Logic in Computer Science
2025-12-09 v1 Category Theory
Abstract
We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor explicit, allowing standard morphism wires to interact with them through a well-defined set of graphical rules. We establish the soundness and completeness of the diagrammatic calculus, and illustrate its expressiveness through examples drawn from category theory, logic and programming language semantics.
Keywords
Cite
@article{arxiv.2512.06499,
title = {String Diagrams for Closed Symmetric Monoidal Categories},
author = {Callum Reader and Alessandro Di Giorgio},
journal= {arXiv preprint arXiv:2512.06499},
year = {2025}
}