Higher Auslander-Reiten sequences via morphisms determined by objects

Abstract

Let be an Ext-finite, Krull-Schmidt and k-linear n-exangulated category with k a commutative artinian ring. In this note, we define two additive subcategories and of in terms of the representable functors from the stable category of to the category of finitely generated k-modules. Moreover, we show that there exists an equivalence between the stable categories of these two full subcategories. Finally, we give some equivalent characterizations on the existence of Auslander-Reiten n-exangles via determined morphisms. These results unify and extend their works by Jiao–Le for exact categories, Zhao–Tan–Huang for extriangulated categories, Xie–Liu–Yang for n-abelian categories.