**Question:** Let $p : E \to B$ be an exponentiable functor of $\infty$-categories. Suppose that for every $b \in B$, the geometric realization of the fiber $|p^{-1}(b)|$ is contractible. Then does $p$ induce an equivalence of geometric realizations $|p| : |E| \to |B|$?

**Notes:**

If $p$ is a locally cartesian fibration or a locally cocartesian fibration, then the answer is

*yes*by Quillen's Theorem A plus the fact that the fibers are reflective in the lax slices (or dually).Since exponentiable fibrations are a common generalization of cartesian and cocartesian fibrations, one might hope for an affirmative answer here.