Recollements and $n$-cotorsion pairs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913256761720832 |
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| author | Cao, Weiqing Wei, Jiaqun Wu, Kaili |
| author_facet | Cao, Weiqing Wei, Jiaqun Wu, Kaili |
| contents | In the present paper, we study the relationships of $n$-cotorsion pairs among three abelian categories in a recollement. Under certain conditions, we present an explicit construction of gluing of $n$-cotorsion pairs in an abelian category $\mathcal{D}$ with respect to $n$-cotorsion pairs in abelian categories $\mathcal{D}^{'}$, $\mathcal{D}^{''}$ respectively. On the other hand, we study the construction of $n$-cotorsion pairs in abelian categories $\mathcal{D}^{'}$, $\mathcal{D}^{''}$ obtained from $n$-cotorsion pairs in an abelian category $\mathcal{D}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_04220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recollements and $n$-cotorsion pairs Cao, Weiqing Wei, Jiaqun Wu, Kaili Category Theory In the present paper, we study the relationships of $n$-cotorsion pairs among three abelian categories in a recollement. Under certain conditions, we present an explicit construction of gluing of $n$-cotorsion pairs in an abelian category $\mathcal{D}$ with respect to $n$-cotorsion pairs in abelian categories $\mathcal{D}^{'}$, $\mathcal{D}^{''}$ respectively. On the other hand, we study the construction of $n$-cotorsion pairs in abelian categories $\mathcal{D}^{'}$, $\mathcal{D}^{''}$ obtained from $n$-cotorsion pairs in an abelian category $\mathcal{D}$. |
| title | Recollements and $n$-cotorsion pairs |
| topic | Category Theory |
| url | https://arxiv.org/abs/2403.04220 |