2021/11/12 by Jian He, Jing He, He, Jian +3 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2111.06522
Let (\mathscrC,𝔼,\mathfraks) be an \rm Ext-finite, Krull-Schmidt and k-linear n-exangulated category with k a commutative artinian ring. In this note, we define two additive subcategories \mathscrCr and \mathscrCl of \mathscrC in terms of the representable functors from the stable category of \mathscrC 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.