Resolutions and stability of $C$-Gorenstein flat modules

Abstract

In this paper, we first investigate the relationship between $\mathcal{W} $-(co)resolutions and $\mathcal{X} $-(co)resolutions for two full subcategories $\mathcal{W} $ and $\mathcal{X} $ of an abelian category with $\mathcal{W} \subseteq \mathcal{X} $. Then some applications are given. In particular, we obtain the stability of the category of $C$-Gorenstein flat modules under the procedure used to define these entities, which is different from that established by Sather-Wagstaff, Sharif and White.