Exact dg categories I : Foundations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909116501327872 |
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| author | Chen, Xiaofa |
| author_facet | Chen, Xiaofa |
| contents | We introduce the notion of exact dg category, which provides a differential graded enhancement of Nakaoka--Palu's notion of extriangulated category. We give a definition in complete analogy with Quillen's but where the category of kernel-cokernel pairs is replaced with a more sophisticated homotopy category. We introduce the notion of stable dg category, and prove that the $H^0$-category of an exact dg category $\mathcal{A}$ is triangulated if and only if $\mathcal{A}$ is stable. We illustrate our theory with several examples including the homotopy category of two-term complexes and Amiot's fundamental domain for generalized cluster categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact dg categories I : Foundations Chen, Xiaofa Representation Theory Category Theory We introduce the notion of exact dg category, which provides a differential graded enhancement of Nakaoka--Palu's notion of extriangulated category. We give a definition in complete analogy with Quillen's but where the category of kernel-cokernel pairs is replaced with a more sophisticated homotopy category. We introduce the notion of stable dg category, and prove that the $H^0$-category of an exact dg category $\mathcal{A}$ is triangulated if and only if $\mathcal{A}$ is stable. We illustrate our theory with several examples including the homotopy category of two-term complexes and Amiot's fundamental domain for generalized cluster categories. |
| title | Exact dg categories I : Foundations |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2402.10694 |