$\V\W$-Gorenstein categories

Authors: GUOQIANG ZHAO, JUXIANG SUN

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

Keywords: ($\V$$\W$-)Gorenstein categories, semidualizing modules, Gorenstein projective modules, Gorenstein injective modules, Bass class

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