Gorenstein homological coalgebras and quasi-Frobenius bicomodules
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In this paper, we prove that the class of Gorenstein coflat comodules is preserved under Frobenius functors. As a generalization of the Frobenius functors and Frobenius morphism of coalgebras, we obtain that if $\varphi:C\rightarrow D$ is a right quasi-Frobenius morphism of coalgebras and $_{D}C$ is a cogenerator, then $X$ is a Gorenstein injective right $C$-comodule if and only if $X$ is a Gorenstein injective right $D$-comodule.
Abstract
In this paper, we prove that the class of Gorenstein coflat comodules is preserved under Frobenius functors. As a generalization of the Frobenius functors and Frobenius morphism of coalgebras, we obtain that if $\varphi:C\rightarrow D$ is a right quasi-Frobenius morphism of coalgebras and $_{D}C$ is a cogenerator, then $X$ is a Gorenstein injective right $C$-comodule if and only if $X$ is a Gorenstein injective right $D$-comodule.