We introduce the right (left) Gorenstein subcategory relative to an additive subcategory $$\mathscr{C}$$ C of an abelian category $$\mathscr{A}$$ A , and prove that the right Gorenstein subcategory rG ( $$\mathcal{G}(\mathscr{C})$$ G ( C ) ) is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When $$\mathscr{C}$$ C is self-orthogonal, we give a characterization for objects in rG ( $$\mathcal{G}(\mathscr{C})$$ G ( C ) ), and prove that any object in $$\mathscr{A}$$ A with finite rG ( $$\mathcal{G}(\mathscr{C})$$ G ( C ) )-projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in $$\mathscr{A}$$ A with finite $$\mathscr{C}$$ C -projective dimension to an object in rG ( $$\mathcal{G}(\mathscr{C})$$ G ( C ) ). As an application, we obtain a weak Auslander-Buchweitz context related to the kernel of a hereditary cotorsion pair in $$\mathscr{A}$$ A having enough injectives.

中文翻译：

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单面 Gorenstein 子类别

我们相对于阿贝尔范畴 $$\mathscr{A}$$ A 的加性子范畴 $$\mathscr{C}$$ C 引入右（左）Gorenstein 子范畴，并证明右 Gorenstein 子范畴 rG ( $$ \mathcal{G}(\mathscr{C})$$ G ( C ) ) 在扩展、同胚核、直接被加数和有限直接和下是封闭的。当 $$\mathscr{C}$$ C 自正交时，我们给出 rG 中对象的表征（ $$\mathcal{G}(\mathscr{C})$$ G ( C ) ），并证明$$\mathscr{A}$$ A 中具有有限 rG ( $$\mathcal{G}(\mathscr{C})$$ G ( C ) )-投影维度的任何对象与核（或核) 从 $$\mathscr{A}$$ A 中的对象到 rG ( $$\mathcal{G}(\mathscr{ C})$$ G ( C ) )。作为应用程序，