2024/09/16 by Vitor Gulisz, Gulisz, Vitor · 2 citations
Mathematics · #16E99 (Secondary) #18A25 (Primary) 18E99 #18E05 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2409.10438
openalex publication_date 2024/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a functorial approach to the study of n-abelian categories by reformulating their axioms in terms of their categories of finitely presented functors. Such an approach allows the use of classical homological algebra and representation theory techniques to understand higher homological algebra. As an application, we present two possible generalizations of the axioms "every monomorphism is a kernel" and "every epimorphism is a cokernel" of an abelian category to n-abelian categories. We also specialize our results to modules over rings, thereby describing when the category of finitely generated projective modules over a ring is n-abelian. Moreover, we establish a correspondence for n-abelian categories with additive generators, which extends the higher Auslander correspondence.