Abstracts.2020.StringDiagrams

String Diagrams

by Robin Adams

Abstract

String diagrams are a beautifully simple language for reasoning in certain categories that make many calculations embarrassingly simple. They seem to have been invented independently several times, as Feynman diagrams and tensor networks. We will never know for sure, because for a long time researchers used them in their rough work but were ashamed to put them in published papers. I will show how string diagrams can be used to reason in braided, symmetric and closed monoidal categories, give translations to and from type theory, and describe their physical application in quantum theory and gauge field theory, among others.

Proof assistants

• Quantomatic
• Globular (web-based)
• homotopy.io (web-based successor to Globular)
• Cartographer (web-based)