Cotorsion pairs in $(d+2)$-angulated categories
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929606240501760 |
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| author | Chang, Huimin Zhou, Panyue |
| author_facet | Chang, Huimin Zhou, Panyue |
| contents | Let $\mathcal C$ be a $(d+2)$-angulated category. In this paper, we define the notions of cotorsion pairs and weak cotorsion pairs in $\mathcal C$, which are generalizations of the classical cotorsion pairs in triangulated categories. As an application, we give a geometric characterization of weak cotorsion pairs in $(d+2)$-angulated cluster categories of type $A$. Moreover, we prove that any mutation of a (weak) cotorsion pair in $\mathcal C$ is again a (weak) cotorsion pair. When $d=1$, this result generalizes the work of Zhou and Zhu on classical cotorsion pairs in triangulated categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cotorsion pairs in $(d+2)$-angulated categories Chang, Huimin Zhou, Panyue Representation Theory Category Theory Let $\mathcal C$ be a $(d+2)$-angulated category. In this paper, we define the notions of cotorsion pairs and weak cotorsion pairs in $\mathcal C$, which are generalizations of the classical cotorsion pairs in triangulated categories. As an application, we give a geometric characterization of weak cotorsion pairs in $(d+2)$-angulated cluster categories of type $A$. Moreover, we prove that any mutation of a (weak) cotorsion pair in $\mathcal C$ is again a (weak) cotorsion pair. When $d=1$, this result generalizes the work of Zhou and Zhu on classical cotorsion pairs in triangulated categories. |
| title | Cotorsion pairs in $(d+2)$-angulated categories |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2411.17975 |