TRANSITIVE 2-REPRESENTATIONS OF FINITARY 2-CATEGORIES

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. 2010 Mathematics Subject Classification. Primary 18D05; Secondary 16D20, 17B10, 16G10.