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arXiv · 2012.03863

Extension Of The 2-Representation Theory Of Finitary 2-Categories To Locally (Graded) Finitary 2-Categories

James Macpherson
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Abstract

We extend the 2-representation theory of finitary 2-categories to certain 2-categories with infinitely many objects, denoted locally finitary 2-categories, and extend the classical classification results of simple transitive 2-representations of weakly fiat 2-categories to this environment. We also consider locally finitary 2-categories and 2-representations with a grading, and prove the associated coalgebra 1-morphisms have a homogeneous structure. We use these results to classify simple transitive 2-representations of certain classes of cyclotomic 2-Kac-Moody algebras.

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James Macpherson. 2020-12-07. Extension Of The 2-Representation Theory Of Finitary 2-Categories To Locally (Graded) Finitary 2-Categories. https://arxiv.org/abs/2012.03863

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