Resolution Dimension Relative To Resolving Subcategories In Extriangulated Categories

Let (C, E, s) be an extriangulated category with a proper class xi of E-triangles and X a resolving subcategory of C. In this paper, we introduce the notion of X-resolution dimension relative to the subcategory X in C, and then give some descriptions of objects with finite X-resolution dimension. In particular, we obtain Auslander-Buchweitz approximations for these objects. As applications, we construct adjoint pairs for two kinds of inclusion functors, and construct a new resolving subcategory from a given resolving subcategory which reformulates some known results.