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Original Articles

Gorenstein coresolving categories

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Pages 4477-4491 | Received 11 Jul 2016, Published online: 25 Mar 2017
 

ABSTRACT

Let π’œ be an abelian category. A subcategory 𝒳 of π’œ is called coresolving if 𝒳 is closed under extensions and cokernels of monomorphisms and contains all injective objects of π’œ. 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 𝒒ℐ𝒳(π’œ). 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 𝒒ℐ𝒳(π’œ) and apply the obtained properties to special subcategories and in particular to module categories.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

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