Generalized diagram categories and monoids, and their representations
arXiv:2512.17177
Abstract
Classical diagram categories and monoids, including the Temperley--Lieb, Brauer, and partition cases, arise as special instances of the category of two dimensional cobordisms and admit additional twists that produce a large new family of diagram categories and monoids. In this paper we introduce this family and develop a unified approach to their representation theory.
45 pages, many figures, comments welcome