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arXiv · 2310.11172

Dimensions and cotorsion pairs in recollements of extriangulated categories

Xin Ma·Panyue Zhou
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Abstract

Let $(\mathcal A, \mathcal B, \mathcal C)$ be a recollement of extriangulated categories. In this paper, we provide bounds on the coresolution dimensions of the subcategories involved in $\mathcal A$, $\mathcal B$ and $\mathcal C$. We show that a hereditary cotorsion pair in $\mathcal B$ can induce hereditary cotorsion pairs in $\mathcal A$ and $\mathcal C$ under certain conditions. Besides, we construct recollements of abelian categories from a recollement of extriangulated categories with respect to the hearts of cotorsion pairs.

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Xin Ma, Panyue Zhou. 2023-10-17. Dimensions and cotorsion pairs in recollements of extriangulated categories. https://arxiv.org/abs/2310.11172

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