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.
Homology, Homotopy and Applications, Vol. 12 (2010), No. 1, pp.187-219.
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