Additive versus abelian 2-representations of fiat 2-categories

Abstract

We study connections between additive and abelian 2-representations of fiat 2-categories, describe combinatorics of 2-categories in terms of multisemigroups and determine the annihilator of a cell 2-representation. We also describe, in detail, examples of fiat 2-categories associated to ${\mathfrak{sl}}_2$-categorification in the sense of Chuang and Rouquier, and 2-categorical analogues of Schur algebras.

20 pages

References in corpus (2)

• 2-Kac-Moody algebras
• Categorification of the braid groups

Cited by in corpus (1)

• Categorification of the Catalan monoid