Homotopy theory of $dg$ categories via localizing pairs and Drinfeld’s $dg$ quotient

Abstract

Using localizing pairs and Drinfeld's dg quotient we construct a new Quillen model for the homotopy theory of dg categories. We prove that, in contrast with the original model, this new Quillen model carries a natural closed symmetric monoidal structure. As an application, we obtain a simple construction of the internal Hom-objects and a conceptual characterization of Toen's previous work. Making use of this new Quillen model, Lowen has recently developed a derived deformation theory.