2025/12/22 by Zetao Lin, Shiping Liu, Lin, Zetao +1
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · doi:10.48550/arxiv.2512.19296
openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
Using the Nakayama duality induced by a Nakayama functor, we provide a novel and concise account of the existence of Auslander-Reiten dualities and almost split sequences in abelian categories with enough projective objects or enough injective objects. As an example, we establish the existence of almost split sequences ending with finitely presented modules and those starting with finitely copresented modules in the category of all modules over a small endo-local Hom-reflexive category. Specializing to algebras given by (not necessarily finite) quivers with relations, we further investigate when the categories of finitely presented modules, finitely copresented modules and finite dimensional modules have almost split sequences on either or both sides.