Quillen equivalence for chain homotopy categories induced by balanced pairs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908984966905856 |
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| author | Hu, Jiangsheng Ren, Wei Yang, Xiaoyan You, Hanyang |
| author_facet | Hu, Jiangsheng Ren, Wei Yang, Xiaoyan You, Hanyang |
| contents | For a balanced pair $(\mathcal{X},\mathcal{Y})$ in an abelian category, we investigate when the chain homotopy categories ${\bf K}(\mathcal{X})$ and ${\bf K}(\mathcal{Y})$ are triangulated equivalent. To this end, we realize these chain homotopy categories as homotopy categories of certain model categories and give conditions that ensure the existence of a Quillen equivalence between the model categories in question. We further give applications to cotorsion triples, Gorenstein projective and Gorenstein injective modules, as well as pure projective and pure injective objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quillen equivalence for chain homotopy categories induced by balanced pairs Hu, Jiangsheng Ren, Wei Yang, Xiaoyan You, Hanyang Representation Theory Category Theory Rings and Algebras For a balanced pair $(\mathcal{X},\mathcal{Y})$ in an abelian category, we investigate when the chain homotopy categories ${\bf K}(\mathcal{X})$ and ${\bf K}(\mathcal{Y})$ are triangulated equivalent. To this end, we realize these chain homotopy categories as homotopy categories of certain model categories and give conditions that ensure the existence of a Quillen equivalence between the model categories in question. We further give applications to cotorsion triples, Gorenstein projective and Gorenstein injective modules, as well as pure projective and pure injective objects. |
| title | Quillen equivalence for chain homotopy categories induced by balanced pairs |
| topic | Representation Theory Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2503.01188 |