Transitive 2-representations of finitary 2-categories

  title={Transitive 2-representations of finitary 2-categories},
  author={Volodymyr Mazorchuk and Vanessa Miemietz},
  journal={Transactions of the American Mathematical Society},
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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