• Journal of the Korean Mathematical Society
• /
• v.60 no.6
• /
• pp.1255-1302
• /
• 2023

We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic nature. The main result is a categorification of the classical desingularization map for singular Artin monoids associated to finite Weyl groups using BGG category 𝒪.