The word problem in linear monoidal categories and applicationsMPIM

by Léo Schelstraete (MPIM)

Thursday Oct 16, 2025, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI-Oberseminar

The word problem asks a fundamental question: given an algebraic structure defined by generators and relations, determine algorithmically whether two “compounds” of those generators are the same under those relations. For algebras, the classical approach is given by Gröbner bases, or more generally, Bergman’s diamond lemma. Solving the word problem in this setting means getting a basis, but also various other structures, including the possibility to compute homological invariants. Nowadays, Gröbner bases are the backbone of computer algebra programs.
Linear monoidal categories are the categorical analogues of algebras. They are ubiquitous in modern-day representation theory and low-dimensional topology. However, their word problem is typically much more involved, and so far, only case-specific techniques are known.
In this talk, I will describe the first steps toward a general approach of the word problem for linear monoidal categories, and sketch the hopes for the future. The techniques come from rewriting theory, with many inspirations from higher category theory.