Quasi-resolving subcategories and dimensions in extriangulated categories

2025/11/10 by He, Zhenggang
#Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.07039

Abstract

Let C=(C,𝔼,\mathfraks) be an extriangulated category with a proper class ξ of 𝔼-triangles. In this paper, we introduce and study quasi-resolving subcategories in C. More precisely, we first introduce the notion of X-resolution dimensions for a quasi-resolving subcategory X of C and then give some equivalent characterizations of objects which have finite X-resolution dimensions. As an application, we introduce Gorenstein quasi-resolving subcategories, denoted by GQP_X(ξ), in term of a quasi-resolving subcategory X, and prove that GQP_X(ξ) is also a quasi-resolving subcategory of C. Moreover, some classical known results are generalized in GQP_X(ξ).

Citations

• Localization of extriangulated categories
• Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories
• Triangulated quotient categories revisited
• Classifying thick subcategories of the stable category of Cohen-Macaulay modules
• Stable module theory

Related

• Relative quasi-Gorensteinness in extriangulated categories
• Gorenstein Derived Functors for Extriangulated Categories
• Gorenstein Objects in Extriangulated Categories
• Proper Resolutions and Gorenstein Categories
• Resolving subcategories and dimensions in recollements of extriangulated categories