2021/12/02 by Jian He, Jing He, He, Jian +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2112.00981
openalex publication_date 2021/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (\mathscrC,𝔼,\mathfraks) be an Ext-finite, Krull-Schmidt and k-linear n-exangulated category with k a commutative artinian ring. In this note, we prove that \mathscrC has Auslander-Reiten-Serre duality if and only if \mathscrC has Auslander-Reiten n-exangles. Moreover, we also give an equivalent condition for the existence of Serre duality (which is a special type of Auslander-Reiten-Serre duality). Finally, assume further that \mathscrC has Auslander-Reiten-Serre duality. We exploit a bijection triangle, which involves the restricted Auslander bijection and the Auslander-Reiten-Serre duality.