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Title
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On the twisted tensor product of small dg categories
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Author
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Abstract
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| Given two small dg categories C;D, defined over a field, we introduce their (nonsymmetric) twisted tensor product C D. We show that D is left adjoint to the functor Coh.D;/, where Coh.D;E/ is the dg category of dg functors D ! E 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 C;D cofibrant, the adjunction descends to the corresponding adjunction in the homotopy category. Then comparison with a result of Toën [33] shows that, for C;D cofibtant, C D is isomorphic to C D, as an object of the homotopy category Hot. |
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Language
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English
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Source (journal)
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Journal of noncommutative geometry
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Publication
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2020
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ISSN
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1661-6952
1661-6960
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DOI
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10.4171/JNCG/380
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Volume/pages
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14
:2
(2020)
, p. 789-820
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ISI
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000556598900012
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Full text (Publisher's DOI)
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Full text (open access)
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