Resolving subcategories and dimensions in recollements of extriangulated categories

TL;DR

This paper studies how to construct resolving subcategories within recollements of extriangulated categories, applying Auslander-Reiten theory to module categories, and establishing bounds on resolution dimensions.

Contribution

It introduces methods for constructing resolving subcategories in recollements of extriangulated categories and explores their applications to cotilting modules and resolution dimensions.

Findings

Methods for constructing resolving subcategories

Gluing of cotilting modules in module categories

Bounds on resolution dimensions in recollements

Abstract

Recently, Wang, Wei and Zhang introduced the notion of recollements of extriangulated categories. In this paper, let $(\mathcal{A},\mathcal{B},\mathcal{C})$ be a recollement of extriangulated categories. We provide some methods to construct resolving subcategories in $(\mathcal{A},\mathcal{B},\mathcal{C})$. As applications of the Auslander-Reiten correspondence, we get the gluing of cotilting modules in a recollement of module categories for artin algebras. We also give some bounds of resolution dimensions of the categories involved in $(\mathcal{A},\mathcal{B},\mathcal{C})$ with respect to resolving subcategories, which generalize some known results.