一个不是$(n+2)$-角范畴的预$(n+2)$-角范畴
A pre-$(n+2)$-angulated category which is not $(n+2)$-angulated
浏览论文内容
中文总结 AI 辅助
本研究构造了一个明确的非9-角的预9-角范畴，以预投射代数$Π(A_5)$的有限生成投射右模范畴为基础，通过扭曲完全比较的奇数次幂实现，为相关蕴涵命题提供了高阶反例。
中文摘要 AI 辅助
我们构造了一个明确的非9-角的预9-角范畴，从而为“预$(n+2)$-角范畴蕴涵$(n+2)$-角范畴”这一命题给出了一个真正的高阶反例。其基础加法范畴是$\text{F}_2$上预投射代数$Π(A_5)$的有限生成投射右模的范畴。该构造通过取Chen-Liu-Lu-Zhang在其预三角反例中使用的扭曲完全比较的奇数次幂，并证明所得的预9-角结构不满足高阶映射锥公理而得到。
英文摘要
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.
发表机构
- Lanzhou University of Technology（兰州理工大学）
机构由 AI 辅助整理，请以论文原文为准。
