Diagrammatic rewriting for category theoristsMPIM

by Léo Schelstraete (MPIM)

Tuesday Jan 27, 2026, 11:00 AM → 12:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Abstract Homotopy Theory Seminar

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).