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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.doi:10.1090/tran/6583 fatcat:cameq6asqrbz5o75ljv5isnnie