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ABSTRACT Let ???? be an abelian category. A subcategory ???? of ???? is called coresolving if ???? is closed under extensions and cokernels of monomorphisms and contains all injective objects… Click to show full abstract
ABSTRACT Let ???? be an abelian category. A subcategory ???? of ???? is called coresolving if ???? is closed under extensions and cokernels of monomorphisms and contains all injective objects of ????. In this paper, we introduce and study Gorenstein coresolving categories, which unify the following notions: Gorenstein injective modules [8], Gorenstein FP-injective modules [20], Gorenstein AC-injective modules [3], and so on. Then we define a resolution dimension relative to the Gorenstein coresolving category ????ℐ????(????). 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 ????ℐ????(????) and apply the obtained properties to special subcategories and in particular to module categories.
Journal Title: Communications in Algebra
Year Published: 2017
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