Stability of Cartan–Eilenberg Gorenstein categories

Abstract

We study Cartan-Eilenberg Gorenstein categories by introducing $\mathrm{CE}$ -projective $\mathrm{CE}$ -generators and $\mathrm{CE}$ -injective $\mathrm{CE}$ -cogenerators in the paper. We give a relationship between injective cogenerators (resp., projective generators) introduced by Sather-Wagstaff, Sharif and White and $\mathrm{CE}$ -injective $\mathrm{CE}$ -cogenerators (resp., $\mathrm{CE}$ -projective $\mathrm{CE}$ -generators). As applications, we prove some stability results of Cartan-Eilenberg Gorenstein categories.