Homology, Homotopy and Applications
Volume 12 (2010)
Homotopy theory of $dg$ categories via localizing pairs and Drinfeld’s $dg$ quotient
Pages: 187 – 219
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 Toën’s previous work. Making use of this new Quillen model, Lowen has recently developed a derived deformation theory.
$dg$ category; localization pair; Drinfeld $dg$ quotient; Quillen model category
2010 Mathematics Subject Classification