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arXiv · 2406.11226

Exact dg categories II : The embedding theorem

Xiaofa Chen
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Abstract

For an exact dg category $\mathcal A$, we introduce its bounded dg derived category $\mathcal{D}^b_{dg}(\mathcal A)$ and establish the universal exact morphism from $\mathcal A$ to $\mathcal{D}^b_{dg}(\mathcal A)$. We prove that the dg quotient of an exact dg category by a subcategory of projective-injectives carries a canonical exact structure. We show that exact dg categories reproduce under tensor products and functor dg categories. We apply our results to 0-Auslander extriangulated categories and confirm a conjecture by Fang-Gorsky-Palu-Plamondon-Pressland for the algebraic case.

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Xiaofa Chen. 2024-06-17. Exact dg categories II : The embedding theorem. https://arxiv.org/abs/2406.11226

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