Model structure arising from one hereditary complete cotorsion pair on extriangulated categories
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914376679686144 |
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| author | Hu, Jiangsheng Zhang, Dongdong Zhang, Pu Zhou, Panyue |
| author_facet | Hu, Jiangsheng Zhang, Dongdong Zhang, Pu Zhou, Panyue |
| contents | Hovey's correspondence between model structures and cotorsion pairs in the setting of abelian categories, has been generalized by Nakaoka-Palu, using two cotorsion pairs, to the setting of weakly idempotent complete extriangulated categories, and the aim of the paper is to give an analogous correspondence using one (hereditary) cotorsion pair generalizing in this setting work of Beligiannis-Reiten and Cui, Lu and Zhang. Furthermore, we provide methods to construct model structures from silting objects in weakly idempotent complete extriangulated categories and co-$t$-structures on triangulated categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Model structure arising from one hereditary complete cotorsion pair on extriangulated categories Hu, Jiangsheng Zhang, Dongdong Zhang, Pu Zhou, Panyue Representation Theory Category Theory Hovey's correspondence between model structures and cotorsion pairs in the setting of abelian categories, has been generalized by Nakaoka-Palu, using two cotorsion pairs, to the setting of weakly idempotent complete extriangulated categories, and the aim of the paper is to give an analogous correspondence using one (hereditary) cotorsion pair generalizing in this setting work of Beligiannis-Reiten and Cui, Lu and Zhang. Furthermore, we provide methods to construct model structures from silting objects in weakly idempotent complete extriangulated categories and co-$t$-structures on triangulated categories. |
| title | Model structure arising from one hereditary complete cotorsion pair on extriangulated categories |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2406.14031 |