Dimensions and cotorsion pairs in recollements of extriangulated categories

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.