# Transitive 2-representations of finitary 2-categories

@article{Mazorchuk2014Transitive2O, title={Transitive 2-representations of finitary 2-categories}, author={Volodymyr Mazorchuk and Vanessa Miemietz}, journal={Transactions of the American Mathematical Society}, year={2014}, volume={368}, pages={7623-7644} }

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-H{\"o}lder 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…

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