Abstract
We prove that categorified quantum sl2 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 sl2 uniquely up to equivalence. As an application we characterize all bimodule homomorphisms in the Flag 2-category and prove that on the homological level the categorified quantum Casimir of sl2 acts appropriately on these 2-representations.
Beliakova, Anna