Homology, Homotopy and Applications

Volume 12 (2010)

Number 1

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

Pages: 187 – 219

DOI: https://dx.doi.org/10.4310/HHA.2010.v12.n1.a11


Gonçalo Tabuada (Departamento de Matemática e CMA, FCT-UNL, Quinta da Torre,Caparica, Portugal)


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

18D20, 18G55

Published 1 January 2010