  This paper is the first step in the project of categorifying the bialgebra
structure on the half of quantum group $U_{q}(\mathfrak{g})$ by using geometry
and Hall algebras. We equip the category of D-modules on the moduli stack of
objects of the category $Rep_{\mathbb{C}}(Q)$ of representations of a quiver
with the structure of an algebra object in the category of stable
$\infty$-categories. The data for this construction is provided by an extension
of the Waldhausen construction for the category $Rep_{\mathbb{C}}(Q)$. We
discuss the connection to the Khovanov-Lauda-Rouquier categorification of half
of the quantum group $U_{q}(\mathfrak{g})$ associated to the quiver $Q$ and
outline our approach to the categorification of the bialgebra structure.
