正则时钟映射与迹空间
Regular clock maps and trace spaces
AI总结：
本文研究正则时钟映射，证明其构成时钟映射范畴的小正交类，从而局部可表现，并证明正则时钟映射下从有向路径到迹的典范商映射是同伦等价。
摘要：
正则时钟映射是从饱和有向空间到有向圆的有向空间的正则映射。我们证明正则时钟映射的范畴是时钟映射范畴的小正交类。因此它是局部可表现的。任何预立方集和横截集的几何实现都产生一个正则时钟映射。最后，我们证明对于正则时钟映射的底层有向空间，从有向路径到迹的典范商映射总是同伦等价。
英文摘要：
A regular clock map is a regular map of directed spaces from a saturated directed space to the directed circle. We prove that the category of regular clock maps is a small-orthogonality class in the category of clock maps. Hence it is locally presentable. The geometric realization of any precubical set or transverse set gives rise to a regular clock map. Finally, we prove that for the underlying directed space of a regular clock map, the canonical quotient from directed paths to traces is always a homotopy equivalence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
