Almost split sequences in morphism categories

Rasool Hafezi

Published 2021-03-16Version 1

The almost split sequences are the main ingredient in the Auslander-Reiten theory. We study the structure of almost split sequences in the morphism category with certain ending terms. The morphism category of the module category of some Artin algebra is recalled to be a category whose objects are morphisms in the module category and its morphisms are given with commutative diagrams. Our results give some new interpretation of some certain morphisms in the module category via the Auslander-Reiten translation of the morphism category. As a consequence, the connection between representation-finite morphism categories and Dynkin diagrams is considered. Further, some applications in concern of the almost split sequences over (stable) Auslander algebras are also established.