… We generalize Ringel and Schmidmeier’s theory on the Auslander–Reiten translation of the
submodule category S2.A/ to the monomorphism category … 1 Basics of morphism categories …

… morphisms are given by commutative squares. Since the morphism category H(Λ) is equivalent
to the category of … result of Auslander and Reiten, we know that almost split sequences …

… For each module C in a category C we denote by C/C the category given by the following
data. The objects in C/C are the morphisms / : X —> C for all X in C. For two objects / : X -> C …

… if every morphism in A has a pseudocokernel. We will usually deal with coherent categories,
… For an object B in a category B we here denote by add B the full subcategory of B whose …

… of the Auslander–Reiten species of C . Finally we prove that any locally finite … an
Auslander–Reiten quiver of some extriangulated category with sink morphisms and source …

… is of finite representation type, whereas the category S(Λ) may … for an Auslander-Reiten type
theory of submodule categories. … For the terminology around almost split morphisms we refer …

… For selfinjective algebras this is an equivalence of categories, which we study in section 5.
A A-module M with no nonzero projective summands is said to be periodic if …

… of morphisms in A from the object X to the object Y. It should he noted that preadditive categories
are the same thing as Z-categories … notions for preadditive categories to R-categories. A …

… of Cohen-Macaulay graded modules with degree zero morphisms. … split sequences in
the category of Cohen-Macaulay modules with degree zero morphisms using the fundamental …

… classes of 0-Auslander exact categories. We will also … morphism category of injective
modules. This enables us to view some known equivalences in terms of morphism categories…