Chains of model structures arising from cotorsion pairs on extriangulated categories
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913062423887872 |
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| author | Sun, Dandan Yang, Xiaoyan Zhang, Dongdong Zhou, Panyue Zhu, Haiyan |
| author_facet | Sun, Dandan Yang, Xiaoyan Zhang, Dongdong Zhou, Panyue Zhu, Haiyan |
| contents | The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Hovey triples whose homotopy categories are equivalent under suitable completeness assumptions, thereby refining results due to El Maaouy and Shao-Wang-Zhang. As an application, we consider objects of finite Gorenstein injective dimension with respect to a proper class of $\mathbb{E}$-triangles. Under mild set-theoretic assumptions, we obtain a chain of model structures whose homotopy categories are all triangulated equivalent to a common stable category. This recovers known results for Gorenstein injective modules and yields new examples in the derived category of a ring when the proper class is given by cohomological ghost triangles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23352 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chains of model structures arising from cotorsion pairs on extriangulated categories Sun, Dandan Yang, Xiaoyan Zhang, Dongdong Zhou, Panyue Zhu, Haiyan Representation Theory Category Theory The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Hovey triples whose homotopy categories are equivalent under suitable completeness assumptions, thereby refining results due to El Maaouy and Shao-Wang-Zhang. As an application, we consider objects of finite Gorenstein injective dimension with respect to a proper class of $\mathbb{E}$-triangles. Under mild set-theoretic assumptions, we obtain a chain of model structures whose homotopy categories are all triangulated equivalent to a common stable category. This recovers known results for Gorenstein injective modules and yields new examples in the derived category of a ring when the proper class is given by cohomological ghost triangles. |
| title | Chains of model structures arising from cotorsion pairs on extriangulated categories |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2604.23352 |