  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.
