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arXiv · 1404.7589

Transitive 2-representations of finitary 2-categories

Volodymyr Mazorchuk·Vanessa Miemietz
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Abstract

In this article, we define and study the class of simple transitive $2$-representations of finitary $2$-categories. We prove a weak version of the classical Jordan-Hölder Theorem where the weak composition subquotients are given by simple transitive $2$-representations. For a large class of finitary $2$-categories we prove that simple transitive $2$-representations are exhausted by cell $2$-representations. Finally, we show that this large class contains finitary quotients of $2$-Kac-Moody algebras.

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BibTeXRIS

Volodymyr Mazorchuk, Vanessa Miemietz. 2015-12-16. Transitive 2-representations of finitary 2-categories. https://arxiv.org/abs/1404.7589

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