Monomorphism categories, cotilting theory, and Gorenstein-projective modules

The monomorphism category Sn(X) is introduced, where X is a full subcategory of the module category A-mod of an Artin algebra A. The key result is a reciprocity of the monomorphism operator Sn and the left perpendicular operator ⊥: for a cotilting A-module T, there is a canonical construction of a cotilting module m(T) over the upper triangular matrix algebra Tn(A), such that .As applications, Sn(X) is a resolving contravariantly finite subcategory in Tn(A)-mod with -mod if and only if X is a resolving contravariantly finite subcategory in A-mod with -mod. For a Gorenstein algebra A, the category Tn(A)-Gproj of Gorenstein-projective Tn(A)-modules can be explicitly determined as . Also, self-injective algebras A can be characterized by the property Tn(A)-Gproj=Sn(A). Finally, we obtain a characterization of those categories Sn(A) which have finite representation type in terms of Auslanderʼs representation dimension.