We develop Tannaka duality theory for dg categories. To any dg functor from a dg category $\mathcal A$ to finite-dimensional complexes, we associate a dg coalgebra $C$ via a Hochschild homology construction. When the dg functor is faithful, this gives a quasi-equivalence between the derived dg categories of $\mathcal A$-modules and of $C$-comodules. When $\mathcal A$ is Morita fibrant (i.e. an idempotent-complete pre-triangulated category), it is thus quasi-equivalent to the derived dg category of compact $C$-comodules. We give several applications for motivic Galois groups.

中文翻译：

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Tannaka对偶性用于增强的三角分类I：重建

我们针对dg类开发了Tannaka对偶理论。对于从dg类别$ \ mathcal A $到有限维络合物的任何dg函子，我们通过Hochschild同源构造将dg代数$ C $关联起来。当dg函子是忠实的时，这会在$ \ mathcal A $ -modules和$ C $ -comodules的派生dg类别之间产生准等价性。当$ \ mathcal A $是Morita纤维状的（即，幂等的预三角分类）时，它与紧凑的$ C $ -comodules的dg类别近似等效。我们为激进的Galois小组提供了几种应用程序。