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 ⋯→ F_1→ F_0→ F^0→ F^1→⋯ of flat comodules with M≅Ker(F^0→ 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)<∞ . Some properties of Gorenstein flat comodules are studied.