On 2-Verma modules for quantum $${\mathfrak {sl}_{2}}$$ sl 2

Abstract

In this paper we study the superalgebra $$A_n$$ , introduced by the authors in previous work on categorification of Verma modules for quantum $${\mathfrak {sl}_{2}}$$ . The superalgebra $$A_n$$ is akin to the nilHecke algebra, and shares similar properties. We also prove a uniqueness result about 2-Verma modules on $$\Bbbk $$ -linear 2-categories.