Decreasing diagrams and coherent presentations

Abstract

We show how decreasing diagrams introduced in the theory of rewriting systems can be used to prove coherence type theorems in category theory. We apply this method to describe a coherent presentation of the $0$-Hecke monoid $\mathcal{H}({\Sigma }_n)$ of the symmetric group ${\Sigma }_n$, i.e. a presentation by generators, relations, and relations between relations.

33p, minor changes to the first version

Cited by in corpus (1)

• An action of the Hecke monoid on rational modules for the Borel subgroup of a quantised general linear group