Transitive 2-representations of finitary 2-categories
Representation Theory
2016-12-30 v3 Category Theory
Abstract
In this article, we define and study the class of simple transitive -representations of finitary -categories. We prove a weak version of the classical Jordan-H\"older Theorem where the weak composition subquotients are given by simple transitive -representations. For a large class of finitary -categories we prove that simple transitive -representations are exhausted by cell -representations. Finally, we show that this large class contains finitary quotients of -Kac-Moody algebras.
Cite
@article{arxiv.1404.7589,
title = {Transitive 2-representations of finitary 2-categories},
author = {Volodymyr Mazorchuk and Vanessa Miemietz},
journal= {arXiv preprint arXiv:1404.7589},
year = {2016}
}
Comments
revised version to appear in Transactions of the AMS, proof of Proposition 22 corrected