$n$-cotorsion pairs and recollements of extriangulated categories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910373560451072 |
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| author | He, Jian He, Jing |
| author_facet | He, Jian He, Jing |
| contents | In this article, we prove that if $(\mathcal A ,\mathcal B,\mathcal C)$ is a recollement of extriangulated categories, then $n$-cotorsion pairs in $\mathcal A$ and $\mathcal C$ can induce $n$-cotorsion pairs in $\mathcal B$. Conversely, this holds true under natural assumptions. Besides, we give mild conditions on a pseudo cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding additive quotients to form a recollement of semi-abelian categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12673 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $n$-cotorsion pairs and recollements of extriangulated categories He, Jian He, Jing Representation Theory Category Theory In this article, we prove that if $(\mathcal A ,\mathcal B,\mathcal C)$ is a recollement of extriangulated categories, then $n$-cotorsion pairs in $\mathcal A$ and $\mathcal C$ can induce $n$-cotorsion pairs in $\mathcal B$. Conversely, this holds true under natural assumptions. Besides, we give mild conditions on a pseudo cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding additive quotients to form a recollement of semi-abelian categories. |
| title | $n$-cotorsion pairs and recollements of extriangulated categories |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2403.12673 |