$\mathcal {W}$-Gorenstein $N$-complexes

Abstract

Given an integer $N\geq 2$ and a self-orthogonal subcategory $\mathcal {W}$ of an abelian category $\mathscr {A}$, we investigate the $\mathcal {W}$-Gorenstein $N$-complexes. We show that an $N$-complex $G$ is $\mathcal {W}$-Gorenstein if and only if $G$ is an $N$-complex consisting of $\mathcal {W}$-Gorenstein objects in $\mathscr {A}$. As an application, we improve a result of Estrada.