Morphisms determined by objects under Galois G-covering theory

Abstract

The theory of morphisms being determined by objects was originally investigated by Auslander, and can be seen as the culmination part of Auslander-Reiten theory. This theory provides a more general frame for working with the Auslander-Reiten theory. In this paper, we will study the behavior of morphisms determined by objects under G-coverings in the sense of Asashiba, which is a generalization of Gabriel's Galois coverings. As an application, we reformulate Bautista and Liu's framework that normal G-coverings preserve sink maps and source maps. We also show that there is a G-covering between two relative stable categories, which unifies Asashiba, Hafezi, Vahed and Mahdavi's work on the stable categories. This is applied to the discussion on the existence of Serre functors by G-coverings of triangulated categories.