Dimensions and cotorsion pairs in recollements of extriangulated categories

Let (A,B,C) be a recollement of extriangulated categories. In this paper, we provide bounds on the coresolution dimensions of the subcategories involved in A, B, and C. We show that a hereditary cotorsion pair in B can induce hereditary cotorsion pairs in A and 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.