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- W2790006788 abstract "Given two small dg categories $C,D$, defined over a field, we introduce their (non-symmetric) twisted tensor product $Coverset{sim}{otimes} D$. We show that $-overset{sim}{otimes} D$ is left adjoint to the functor $Coh(D,-)$, where $Coh(D,E)$ is the dg category of dg functors $Dto E$ and their coherent natural transformations. This adjunction holds in the category of small dg categories (not in the homotopy category of dg categories $mathrm{Hot}$). We show that for $C,D$ cofibrant, the adjunction descends to the corresponding adjunction in the homotopy category. Then comparison with a result of Toen shows that, for $C,D$ cofibtant, $Coverset{sim}{otimes} D$ is isomorphic to $Cotimes D$, as an object of the homotopy category $mathrm{Hot}$." @default.
- W2790006788 created "2018-03-29" @default.
- W2790006788 creator A5085727267 @default.
- W2790006788 date "2018-03-03" @default.
- W2790006788 modified "2023-09-27" @default.
- W2790006788 title "On the twisted tensor product of small dg categories." @default.
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