Morphism Categories of Gorenstein-projective Modules

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