Verdier quotients of stable quasi-categories are localizations

Abstract

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.

19 pages. Comments welcome

References in corpus (1)

• Six model structures for DG-modules over DGAs: Model category theory in homological action