AI 中文总结
针对Chen等人构造的预三角化范畴中八面体公理失效的问题，引入右预三角化范畴的通用扩张构造，得到一个非右三角化的右预三角化范畴。
AI 中文摘要
Chen、Liu、Lu和Zhang近期构造了一个带有可逆平移函子的预三角化范畴，其中Verdier八面体公理不成立。我们引入右预三角化范畴的通用扩张构造，证明该构造保持公理(RTR1)-(RTR3)，而遗忘函子可检测到(RTR4)的失效。将其应用于A₅型例子，该构造得到一个非右三角化的右预三角化范畴，此例中平移函子是忠实的但非本质满射。
英文摘要
Chen, Liu, Lu, and Zhang recently constructed a pretriangulated category with invertible suspension in which Verdier's octahedral axiom fails. We introduce a general enlargement construction for right pretriangulated categories and show that it preserves axioms (RTR1)-(RTR3), while failure of (RTR4) is detected by the forgetful functor. Applied to their type $A_5$ example, the construction yields a right pretriangulated category that is not right triangulated. In this example, the suspension is faithful but not essentially surjective.
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