  We show that the definition and many useful properties of Soergel's functor
$\mathbb{V}$ extend to "universal" variants of the BGG category $\mathcal{O}$,
such as the category which drops the semisimplicity condition on the Cartan
action. We show that this functor naturally factors through a quotient known as
the nondegenerate quotient and show that this quotient admits a "Gelfand-Graev"
action of the Weyl group. Although these categories are not finite length in
any sense, we explicitly compute the kernel of this functor in a universal case
and use this to extend these results to an arbitrary DG category with an action
of a reductive group.
  Along the way, we prove a result which may be of independent interest, which
says that a functor of $G$-categories with a continuous adjoint is an
equivalence if and only if it is an equivalence at each field-valued point,
strengthening a result of Ben-Zvi--Gunningham--Orem.
