Homology, Homotopy and Applications

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

Gonçalo Tabuada

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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 Toën's previous work. Making use of this new Quillen model, Lowen has recently developed a derived deformation theory.

Article information

Source
Homology Homotopy Appl., Volume 12, Number 1 (2010), 187-219.

Dates
First available in Project Euclid: 28 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1296223827

Mathematical Reviews number (MathSciNet)
MR2607415

Zentralblatt MATH identifier
1278.18015

Subjects
Primary: 18D20: Enriched categories (over closed or monoidal categories) 18G55: Homotopical algebra

Keywords
dg category localization pair Drinfeld dg quotient Quillen model category

Citation

Tabuada, Gonçalo. Homotopy theory of dg categories via localizing pairs and Drinfeld's dg quotient. Homology Homotopy Appl. 12 (2010), no. 1, 187--219. https://projecteuclid.org/euclid.hha/1296223827


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