ABSTRACT
Let π be an abelian category. A subcategory π³ of π is called coresolving if π³ is closed under extensions and cokernels of monomorphisms and contains all injective objects of π. In this paper, we introduce and study Gorenstein coresolving categories, which unify the following notions: Gorenstein injective modules [Citation8], Gorenstein FP-injective modules [Citation20], Gorenstein AC-injective modules [Citation3], and so on. Then we define a resolution dimension relative to the Gorenstein coresolving category π’βπ³(π). We investigate the properties of the homological dimension and unify some important properties possessed by some known homological dimensions. In addition, we study stability of the Gorenstein coresolving category π’βπ³(π) and apply the obtained properties to special subcategories and in particular to module categories.