Quasi-resolving subcategories and dimensions in extriangulated categories

Paper

Abstract

Let

be an extriangulated category with a proper class

-triangles. In this paper, we introduce and study quasi-resolving subcategories in

. More precisely, we first introduce the notion of

-resolution dimensions for a quasi-resolving subcategory

and then give some equivalent characterizations of objects which have finite

-resolution dimensions. As an application, we introduce Gorenstein quasi-resolving subcategories, denoted by

, in term of a quasi-resolving subcategory

, and prove that

is also a quasi-resolving subcategory of

. Moreover, some classical known results are generalized in