Gorenstein objects in the category of N-complexes

Abstract

For an integer [Formula: see text] and three subcategories [Formula: see text] of modules, we study the notion of [Formula: see text]-Gorenstein [Formula: see text]-complexes. We show that under certain hypotheses, an [Formula: see text]-complex [Formula: see text] is [Formula: see text]-Gorenstein if and only if [Formula: see text] is a [Formula: see text]-Gorenstein module for each [Formula: see text], [Formula: see text] and [Formula: see text] are [Formula: see text]-acyclic for any [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] denote the subcategory of [Formula: see text][Formula: see text]-complexes and [Formula: see text][Formula: see text]-complexes, respectively. Also, the stability of [Formula: see text]-Gorenstein [Formula: see text]-complexes is considered. As applications, not only some known results are encompassed, but also some new results are obtained, for instance, some equivalent characterizations for Ding injective [Formula: see text]-complexes and Gorenstein AC-injective [Formula: see text]-complexes are given.