Diagrammatic rewriting for category theorists

Monoidal categories, informally known as “diagrammatic algebras”, are ubiquitous in representation theory and low-dimensional topology. Diagrammatic algebras are often described by generators and relations, leading to the “word problem”: given two composite cells in the generators, how to tell if they are related by a sequence of relations? For algebras, the solution is known as Gröbner bases, and more generally, as rewriting theory.

In this talk, I will explain how to extend rewriting theory higher, motivated by diagrammatic algebras. Emphasis will be put on various ideas coming from higher category theory (polygraphs, semistrict categories, double categories).