On the twisted tensor product of small dg categories

  • Boris Shoikhet

    University of Antwerpen, Belgium and National Research University Higher School of Economics, Moscow, Russia
On the twisted tensor product of small dg categories cover

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Abstract

Given two small dg categories , defined over a field, we introduce their (non-symmetric) twisted tensor product . We show that is left adjoint to the functor , where is the dg category of dg functors and their coherent natural transformations. This adjunction holds in the category of small dg categories (not in the homotopy category of dg categories Hot). We show that for cofibrant, the adjunction descends to the corresponding adjunction in the homotopy category. Then comparison with a result of Toën [33] shows that, for cofibrant, is isomorphic to , as an object of the homotopy category Hot.

Cite this article

Boris Shoikhet, On the twisted tensor product of small dg categories. J. Noncommut. Geom. 14 (2020), no. 2, pp. 789–820

DOI 10.4171/JNCG/380