2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124351We define and give axioms for Garside and locally Garside categories. We give an application to Coxeter and Artin groups and Deligne-Lusztig varieties.We have fixed some errors pointed to us by E. Godelle and P. Dehornoy and added new results in section 8Group TheoryRepresentation Theory20F36Garside and locally Garside categoriestext