  The Verdier quotient $\mathcal{T}/\mathcal{S}$ of a triangulated category
$\mathcal{T}$ by a triangulated subcategory $\mathcal{S}$ is defined by a
universal property with respect to triangulated functors out of $\mathcal{T}$.
However, $\mathcal{T}/\mathcal{S}$ is in fact a localization of $\mathcal{T}$,
i.e., it is obtained from $\mathcal{T}$ by formally inverting a class of
morphisms. We establish the analogous result for small stable quasi-categories.
As an application, we explore the compatibility of Verdier quotients with
symmetric monoidal structures. In particular, we record a few useful elementary
results on the quasi-categories associated with symmetric monoidal differential
graded categories and derived categories of symmetric monoidal Abelian
categories for which we were unable to locate proofs in the literature.
