2023/10/18 by Anders S. Kortegaard, Kortegaard, Anders S.
Mathematics · #18E10 #18G80 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2310.12045
openalex publication_date 2023/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathscrA be an extension closed proper abelian subcategory of a triangulated category \mathscrT, with no negative 1 and 2 extensions. From this, two functors from Σ\mathscrA∗\mathscrA to \mathscrA can be constructed giving a snake lemma mirroring that of homology without needing a t-structure. We generalize the concept of intermediate categories, which originates from a paper by Enomoto and Saito, to the setting of proper abelian subcategories and show that under certain assumptions this collection is in bijection with torsion-free classes in \mathscrA.