AI 中文总结
本文证明单一对象生成的泛刚性幺半范畴存在阿贝尔包络，从而否定了每个阿贝尔包络都有商性质的猜想，方法基于幺半Ringel对偶与连续式。
AI 中文摘要
我们证明，由单一对象生成的泛刚性幺半范畴具有阿贝尔包络。由于Coulembier-Etingof-Ostrik-Pauwels（2023）已证明该范畴不能具有满足商性质的阿贝尔包络，这一结果否定了[此 http URL.]中的猜想，该猜想声称每个阿贝尔包络都具有商性质。幺半Ringel对偶（Flake-Gruber arXiv:2512.19558）给出了一个候选包络，作为下有限最高权范畴。我们证明其为阿贝尔包络的论证依赖于Coulembier-Etingof（2024）的连续式来证明所需的泛性质。人工智能被用于发现这些结果。
英文摘要
We show that the universal rigid monoidal category on one object has an abelian envelope. Since it was proven by Coulembier-Etingof-Ostrik-Pauwels (2023) that this category cannot have an abelian envelope with the quotient property, this disproves the conjecture in [op.cit.] saying that every abelian envelope has the quotient property. Monoidal Ringel duality (Flake-Gruber arxiv:2512.19558) yields a candidate envelope as a lower finite highest weight category. Our proof that this is an abelian envelope relies on Coulembier-Etingof's (2024) continuants to show the required universal property. AI was used to find these results.
