Mutation of $n$-cotorsion pairs in extriangulated categories
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916800886734848 |
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| author | Chang, Huimin Liu, Yu Zhou, Panyue |
| author_facet | Chang, Huimin Liu, Yu Zhou, Panyue |
| contents | In this article, we introduce the notion of $n$-cotorsion pairs in extriangulated categories, which extends both the cotorsion pairs established by Nakaoka and Palu and the $n$-cotorsion pairs in triangulated categories developed by Chang and Zhou. We further prove that any mutation of an $n$-cotorsion pair remains an $n$-cotorsion pair. As applications, we provide a geometric characterization of $n$-cotorsion pairs in $n$-cluster categories of type $A_{\infty}$, and we realize mutations of $n$-cotorsion pairs geometrically via rotations of certain configurations of $n$-admissible arcs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mutation of $n$-cotorsion pairs in extriangulated categories Chang, Huimin Liu, Yu Zhou, Panyue Representation Theory Category Theory In this article, we introduce the notion of $n$-cotorsion pairs in extriangulated categories, which extends both the cotorsion pairs established by Nakaoka and Palu and the $n$-cotorsion pairs in triangulated categories developed by Chang and Zhou. We further prove that any mutation of an $n$-cotorsion pair remains an $n$-cotorsion pair. As applications, we provide a geometric characterization of $n$-cotorsion pairs in $n$-cluster categories of type $A_{\infty}$, and we realize mutations of $n$-cotorsion pairs geometrically via rotations of certain configurations of $n$-admissible arcs. |
| title | Mutation of $n$-cotorsion pairs in extriangulated categories |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2506.16188 |