Morphism Categories of Gorenstein-projective Modules

Let Lambda be an algebra of finite Cohen-Macaulay type and Gamma its Cohen-Macaulay Auslander algebra. We are going to characterize the morphism category Mor(Lambda-Gproj) of Gorenstein-projective Lambda-modules in terms of the module category Gamma-mod by a categorical equivalence. Based on this, we obtain that some factor category of the epimorphism category Epi(Lambda-Gproj) is a Frobenius category, and also, we clarify the relations among Mor(Lambda-Gproj), Mor(T-2(Lambda)-Gproj) and Mor(Lambda-Gproj), where T-2(Lambda) and Lambda are respectively the lower triangular matrix algebra and the Morita ring closely related to Lambda.