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arXiv · 2608.29221

A pre-$(n+2)$-angulated category which is not $(n+2)$-angulated

Jian He·Jing He·Panyue Zhou
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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 $\Pi(A_5)$ 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.

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BibTeXRIS

Jian He, Jing He, Panyue Zhou. 2026-08-29. A pre-$(n+2)$-angulated category which is not $(n+2)$-angulated. https://arxiv.org/abs/2608.29221

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