发表机构
Université Paris Cité; CNRS; IRIF（巴黎西岱大学; 法国国家科学研究中心; IRIF研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对有向空间，引入广义时钟概念，构造包含立方时钟的球状时钟，证明定时空间商映射为平凡纤维化，并给出执行路径商定理的新证明。
AI 中文摘要
对于一般的有向空间，遗忘路径的参数化可能会改变其同伦类型。时钟是一个具有亚可度量底空间的有向空间；定时空间是一个配备到时钟的正则有向映射的饱和有向空间。在每一个固定的时钟上，定时空间构成一个局部可表现范畴，并且从固定端点的有向路径到迹的商映射是带有连续截面的平凡Hurewicz纤维化。对于具有可度量拟紧子空间的Hausdorff饱和有向空间，这些商映射是平凡的q-纤维化；这包括第二可数情形。有向圆是立方时钟，但一个有限的胞腔球状例子不存在到它的正则映射。我们从终端多点$d$-空间的胞腔q-余纤维化替换构造了一个球状时钟。它通过一个内射有向映射包含立方时钟，并且从所有q-余纤维化球状实现（它们本身是饱和时钟）接受正则映射。因此，在这个时钟上的定时空间既包括立方例子也包括球状例子。规范化给出了q-余纤维化多点$d$-空间执行路径的商定理的新证明，并证明了按非降满射的商是带有连续截面的平凡Hurewicz纤维化。
英文摘要
For a general directed space, forgetting the parametrization of paths can change their homotopy type. A clock is a directed space with submetrizable underlying space; a timed space is a saturated directed space equipped with a regular directed map to a clock. Over every fixed clock, timed spaces form a locally presentable category, and their quotients from directed paths with fixed endpoints to traces are trivial Hurewicz fibrations with continuous sections. For Hausdorff saturated directed spaces with metrizable quasicompact subspaces, these quotients are trivial q-fibrations; this includes the second countable case. The directed circle is the cubical clock, but a finite cellular globular example admits no regular map to it. We construct a globular clock from a cellular q-cofibrant replacement of the terminal multipointed $d$-space. It contains the cubical clock by an injective directed map and admits regular maps from all q-cofibrant globular realizations, which are themselves saturated clocks. Thus timed spaces over this clock include both cubical and globular examples. Normalization gives a new proof of the quotient theorem for execution paths of q-cofibrant multipointed $d$-spaces and proves that the quotient by nondecreasing surjections is a trivial Hurewicz fibration with a continuous section.
Comments38 pages; 6 figures; generalization of arXiv:2606.02478 by introducing globular clocks
