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

TL;DR

This paper demonstrates that categorified quantum sl(2) can be constructed as an inverse limit of Flag 2-categories derived from cohomology rings, providing a universal property and characterizing bimodule homomorphisms.

Contribution

It introduces a novel inverse limit construction of categorified quantum sl(2) using Flag 2-categories and establishes its universal property within a bicategory framework.

Findings

Characterization of bimodule homomorphisms in Flag 2-category

Categorified quantum Casimir acts correctly on 2-representations

Inverse limit construction provides a unique categorification of quantum sl(2)

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.