  We describe a new type of $2$-representations, using coherent sheaves.
Feigin, Finkelberg, Kuznetsov, Mirkovi\'c and Braverman have provided a
construction of Verma modules for complex semi-simple Lie algebras using based
quasi-map spaces from $\mathbb{P}^1$ to flag varieties (zastavas). We consider
here the case of $\mathfrak{sl}_2$, where the zastavas are smooth, and are mere
affine spaces. We show that coherent sheaves on zastavas provide a $2$-Verma
module for $\mathfrak{sl}_2$ in the sense of Naisse-Vaz. Adding a
superpotential and considering matrix factorizations, we obtain a realization
of simple $2$-representations of $\mathfrak{sl}_2$.
