Moscow Mathematical Journal

Volume 14, Issue 3, July–September 2014 pp. 595–615.

Additive versus abelian 2-Representations of Fiat 2-Categories

Authors: V. Mazorchuk (1) and V. Miemietz (2)
Author institution:(1) Department of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, SWEDEN
(2) School of Mathematics, University of East Anglia, Norwich, UK, NR4 7TJ

Summary:

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 2representation. We also describe, in detail, examples of fiat 2-categories associated to 𝔰𝔩₂-categorification in the sense of Chuang and Rouquier, and 2-categorical analogues of Schur algebras.

2010 Mathematics Subject Classification. 18D05, 18E05, 17B10.

Keywords: 2-category, 2-representation, functor, natural transformation, additive category, abelian category.

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