Coherent presentations of monoids with a right-noetherian Garside family

Pierre-Louis Curien (1, 2) , Alen Ðurić (1, 2) , Yves Guiraud (3, 4)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 PI.R2 - Design, study and implementation of languages for proofs and programs
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
4 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs

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.

Mots clés: Monoid; Coherent presentation; Higher rewriting; Polygraph; Artin-Tits monoid; Garside family

Domaines: Théorie des groupes [math.GR]; Catégories et ensembles [math.CT]

Pierre-Louis Curien, Alen Ðurić, Yves Guiraud. Coherent presentations of monoids with a right-noetherian Garside family. Journal of Homotopy and Related Structures, In press. ⟨hal-03276119v3⟩