Coherent presentations of monoids with a right-noetherian Garside family

TL;DR

This paper develops a method to construct coherent presentations for monoids with a right-noetherian Garside family, unifying previous approaches for Artin-Tits and Garside monoids, and applies it to new classes of monoids.

Contribution

It introduces a general construction of coherent presentations for monoids with a right-noetherian Garside family, extending existing frameworks to broader classes.

Findings

Constructed coherent presentations for a wide class of monoids.

Unified previous methods for Artin-Tits and Garside monoids.

Applied the construction to monoids outside these classes.

Abstract

This paper shows how to construct coherent presentations (presentations by generators, relations and relations among relations) of monoids admitting a right-noetherian Garside family. Thereby, it resolves the question of finding a unifying generalisation of the following two distinct extensions of construction of coherent presentations for spherical Artin-Tits monoids: to general Artin-Tits monoids, and to Garside monoids. The result is applied to some monoids which are neither Artin-Tits nor Garside.