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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.05051 |
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| _version_ | 1866908801281556480 |
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| author | Shao, Qingyu Wang, Junpeng Zhang, Xiaoxiang |
| author_facet | Shao, Qingyu Wang, Junpeng Zhang, Xiaoxiang |
| contents | The aim of this paper is to construct exact model structures from so called extendable cotorsion pairs. Given a hereditary Hovey triple $(\mathcal{C}, \mathcal{W}, \mathcal{F})$ in a weakly idempotent complete exact category with enough projectives and injectives. If one of the cotorsion pairs $(\mathcal{C}\cap\mathcal{W}, \mathcal{F})$ and $(\mathcal{C}, \mathcal{W}\cap\mathcal{F})$ is extendable, then there is a chain of hereditary Hovey triples whose corresponding homotopy categories coincide. As applications, we obtain a new description of the $Q$-shaped derived categories introduced by Holm and Jørgensen. We can also interpret the Krause's recollement in terms of ``$n$-dimensional'' homotopy categories. Finally, we have two approaches to get ``$n$-dimensional'' hereditary Hovey triples, which are proved to coincide, in the category Rep$(Q,\mathcal{A})$ of all representations of a rooted quiver $Q$ with values in an abelian category $\mathcal{A}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Model Structures Arising from Extendable Cotorsion Pairs Shao, Qingyu Wang, Junpeng Zhang, Xiaoxiang Category Theory 18N40, 18G20, 16E35, 16G20 The aim of this paper is to construct exact model structures from so called extendable cotorsion pairs. Given a hereditary Hovey triple $(\mathcal{C}, \mathcal{W}, \mathcal{F})$ in a weakly idempotent complete exact category with enough projectives and injectives. If one of the cotorsion pairs $(\mathcal{C}\cap\mathcal{W}, \mathcal{F})$ and $(\mathcal{C}, \mathcal{W}\cap\mathcal{F})$ is extendable, then there is a chain of hereditary Hovey triples whose corresponding homotopy categories coincide. As applications, we obtain a new description of the $Q$-shaped derived categories introduced by Holm and Jørgensen. We can also interpret the Krause's recollement in terms of ``$n$-dimensional'' homotopy categories. Finally, we have two approaches to get ``$n$-dimensional'' hereditary Hovey triples, which are proved to coincide, in the category Rep$(Q,\mathcal{A})$ of all representations of a rooted quiver $Q$ with values in an abelian category $\mathcal{A}$. |
| title | Model Structures Arising from Extendable Cotorsion Pairs |
| topic | Category Theory 18N40, 18G20, 16E35, 16G20 |
| url | https://arxiv.org/abs/2505.05051 |