Morphism Categories of Gorenstein-projective Modules

Abstract

Let Λ be an algebra of finite Cohen-Macaulay type and Γ its Cohen-Macaulay Auslander algebra. We are going to characterize the morphism category Mor(Λ-Gproj) of Gorenstein-projective Λ-modules in terms of the module category Γ-mod by a categorical equivalence. Based on this, we obtain that some factor category of the epimorphism category Epi(Λ-Gproj) is a Frobenius category, and also, we clarify the relations among Mor(Λ-Gproj), Mor(T2Λ-Gproj) and Mor(Δ-Gproj), where T2(Λ) and Δ are respectively the lower triangular matrix algebra and the Morita ring closely related to Λ.