Generalized diagram categories and monoids, and their representations

Published 19 Dec 2025 in math.RT, math.CO, and math.GR | (2512.17177v1)

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.

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