\(\mathcal{W}\)-Gorenstein \(N\)-complexes
Let \(\mathcal{A}\) be an abelian category with enough projectives and injectives, and let \(\mathcal{W}\) be a self-orthogonal subcategory of \(\mathcal{A}\) in the sense of \textit{S. Sather-Wagstaff} et al. [J. Lond. Math. Soc., II. Ser. 77, No. 2, 481--502 (2008; Zbl 1140.18010)]. The main result of the paper says that if \(G\) is an \(N\)-complex in \(\mathcal{A}\) (where \(N\geq 2\)), then \(G\) is a \(\mathcal{W}\)-Gorenstein \(N\)-complex if and only if \(G\) consists of \(\mathcal{W}\)-Gorenstein objects in \(\mathcal{A}\). As an application it is obtained that if \(R\) is a ring, then an \(N\)-complex of \(R\)-modules is Gorenstein injective if and only if it consists of Gorenstein injective modules.
\(\mathcal{W}\)-Gorenstein \(N\)-complex
scientific article; zbMATH DE number 7136589
scientific article