Categorified quantum sl(2) is an inverse limit of flag 2-categories

Abstract

We prove that categorified quantum sl(2) is an inverse limit of Flag 2-categories defined using cohomology rings of iterated flag varieties. This inverse limit is an instance of a 2-limit in a bicategory giving rise to a universal property that characterizes the categorification of quantum sl(2) uniquely up to equivalence. As an application we characterize all bimodule homomorphisms in the Flag 2-category and prove that the categorified quantum Casimir of sl(2) acts appropriately on these 2-representations.