Gorenstein Flat Comodules

In this paper, we introduce the concept of Gorenstein flat comodules and give a description of colocalization of Gorenstein flat comodules. A right C-comodule M is called a Gorenstein flat comodule if there exists an exact sequence \cdots \rightarrow F_{1}\rightarrow F_{0}\rightarrow F^{0}\rightarrow F^{1}\rightarrow\cdots of flat comodules with M\cong Ker(F^{0}\rightarrow F^{1}) and such that Com_{C}(-,I) leaves the sequence exact whenever I is a finite dimensional right C-comodule and id_{C}(I)\infty. Some properties of Gorenstein flat comodules are studied.