2021/08/10 by Carlo Klapproth, Klapproth, Carlo · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 18G99 #Representation Theory (math.RT) #Secondary 18G80
paper · pdf · doi:10.48550/arxiv.2108.04596
openalex publication_date 2021/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathscrF be an (n+2)-angulated Krull-Schmidt category and \mathscrA ⊂ \mathscrF an n-extension closed, additive and full subcategory with Hom_\mathscrF(Σn \mathscrA, \mathscrA) = 0. Then \mathscrA naturally carries the structure of an n-exact category in the sense of Jasso, arising from short (n+2)-angles in \mathscrF with objects in \mathscrA and there is a binatural and bilinear isomorphism YExtn_(\mathscrA,\mathscrE_\mathscrA)(An+1,A0) ≅ Hom_\mathscrF(An+1, Σn A0) for A0, An+1 ∈ \mathscrA. For n = 1 this has been shown by Dyer and we generalize this result to the case n > 1. On the journey to this result, we also develop a technique for harvesting information from the higher octahedral axiom (N4*) as defined by Bergh and Thaule. Additionally, we show that the axiom (F3) for pre-(n+2)-angulated categories, introduced by Geiss, Keller and Oppermann and stating that a commutative square can be extended to a morphism of (n+2)-angles, implies a stronger version of itself.