  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. In particular, we prove a uniqueness result about
2-Verma modules on $\Bbbk$-linear 2-categories.
