一句话：提出弱化迹幺半范畴的范畴框架，为含闭合类时曲线的量子过程理论提供统一语义。
该文研究在允许时间旅行、即出现闭合类时曲线（CTC）的时空中，量子理论及其他过程理论应如何获得组合式语义。作者对迹对称幺半范畴的定义进行弱化：放弃 yanking 公理，并取消迹需对所有态射有定义的要求，从而建立可容纳时序违反的一般范畴框架。基于该框架，论文统一刻画了两个主流 CTC 量子模型，即 Lloyd 等人的 P-CTC 模型和 Deutsch 的 D-CTC 模型，并首次给出 D-CTC 模型的组合式描述。关键结果是：D-CTC 对应一种尊重相对论因果约束的过程理论，而 P-CTC 通过迹实现 CTC，允许确定性地进行后选择，二者形成鲜明对比。
We introduce a general categorical framework to reason about quantum theory and other process theories living in spacetimes where chronology violation can occur-e.g. in the form of Closed Timelike Curves (CTCs)-allowing resources to travel back in time and provide computational speedups. Our framework is based on a weakening of the definition of traced symmetric monoidal categories, obtained by dropping the yanking axiom and the requirement that the trace be defined on all morphisms. We show that the two leading models for quantum theory with closed timelike curves-namely the P-CTC model of Lloyd et al. and the D-CTC model of Deutsch-are captured by our framework, and in doing so we provide the first compositional description of the D-CTC model. Our description of the D-CTC model results in a process theory which respects the constraints of relativistic causality: this is in direct contrast to the P-CTC model, where CTCs are implemented by a trace and allow post-selection to be performed deterministically.