Exact dg categories II : The embedding theorem
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913393358667776 |
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| author | Chen, Xiaofa |
| author_facet | Chen, Xiaofa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact dg categories II : The embedding theorem Chen, Xiaofa Representation Theory Category Theory K-Theory and Homology 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. |
| title | Exact dg categories II : The embedding theorem |
| topic | Representation Theory Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2406.11226 |