2013/05/08 by Alex Martsinkovsky, Martsinkovsky, Alex · 2 citations
Mathematics · Medicine · #18A25 #18G15 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1305.1914
openalex publication_date 2013/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that direct summands of certain additive functors arising as bifunctors with a fixed argument in an abelian category are again of that form whenever the fixed argument has finite length or, more generally, satisfies the descending chain condition on images of nested endomorphisms. In particular, this provides a positive answer to a conjecture of M. Auslander in the case of categories of finite modules over artin algebras. This implies that the covariant Ext functors are the only injectives in the category of defect-zero finitely presented functors on such categories.