Abstract
Let A be an abelian category, and V , W two additive full subcategories of A. We introduce and study the VW -Gorenstein subcategory of A , which unies many known notions, such as the Gorenstein category and the category consisting of GC -projective (injective) modules, although they were dened in a different way. We also prove that the Bass class with respect to a semidualizing module is one kind of VW -Gorenstein category. The connections between VW -Gorenstein categories and Gorenstein categories are discussed. Some applications are given.
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