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arXiv · 2608.09777

A pre-triangulated category which is not triangulated

Xiao-Wu Chen·Jian Liu·Xue-Song Lu·Chencheng Zhang
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Abstract

In this article, we construct an explicit pre-triangulated category which is not a triangulated category. Its underlying additive category is the category of finitely generated projective modules of the type-$A_5$ preprojective algebra over $\mathbb F_2$, and the suspension is induced by the graph-reflection automorphism.

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Xiao-Wu Chen, Jian Liu, Xue-Song Lu, Chencheng Zhang. 2026-08-10. A pre-triangulated category which is not triangulated. https://arxiv.org/abs/2608.09777

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