… 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 …

… Let C be an arbitrary category, not necessarily a category of modules. For each pair of objects
C\ and C2 in C we denote the set of morphisms from C\ to C2 by C(Ci, C2). For each C in …

… 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 …

… The category A is said to be coherent if every morphism in A has a pseudokernel. Dually, A
… if every morphism in A has a pseudocokernel. We will usually deal with coherent categories, …

… 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 …

… Y) denotes the group 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 where Z is the ring of integers. …

… We denote by mod A/V_ the category whose objects are the same as the objects in mod A,
&nd where the morphisms are given by Hornmod A/X (A,B) = HomA(A,B)/!L(A,B), where ~ ( A , …

… 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…

… we want to consider a morphism f as a morphism in the stable category we use the notation
f… precoverings of the morphism categories and monomorphism categories which are induced …