Additive versus abelian 2-representations of fiat 2-categories

Details Additive versus abelian 2-representations of fiat 2-categories Additive versus abelian 2-representations of fiat 2-categories

2011-12-21

arxiv.org/abs/1112.4949v1

Mathematics

Representation Theory

20 pages

Scientific paper

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.

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