Year: 2026
Type: preprint
Abstract: We construct an explicit pre-$9$-angulated category which is not $9$-angulated, thereby giving a genuinely higher counterexample to the implication from pre-$(n+2)$-angulated to $(n+2)$-angulated. The underlying additive category is the category of finitely generated projective right modules over the preprojective algebra $Π(A_5)$ over $\mathbb F_2$. The construction is obtained by taking an odd power of the twisted complete comparison used by Chen-Liu-Lu-Zhang in their pre-triangulated counterexample and by showing that the resulting pre-$9$-angulation fails the higher mapping-cone axiom.
Source: arXiv (Cornell University)
Authors: He, Jian, He, Jing, Zhou, Panyue
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2271735553
OpenAlex ID: W7204884269