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arXiv · 2104.04924

Torsion pairs and recollements of extriangulated categories

Jian He·Yonggang Hu·Panyue Zhou
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Abstract

In this article, we prove that if $(\mathcal A ,\mathcal B,\mathcal C)$ is a recollement of extriangulated categories, then torsion pairs in $\mathcal A$ and $\mathcal C$ can induce torsion pairs in $\mathcal B$, and the converse holds under natural assumptions. Besides, we give mild conditions on a cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding abelian quotients to form a recollement of abelian categories.

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BibTeXRIS

Jian He, Yonggang Hu, Panyue Zhou. 2021-04-11. Torsion pairs and recollements of extriangulated categories. https://arxiv.org/abs/2104.04924

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