Regular clock map and trace space
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911742125146112 |
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| author | Gaucher, Philippe |
| author_facet | Gaucher, Philippe |
| contents | 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 of the category of clock maps. Hence it is locally presentable. Any geometric realization of precubical sets and of transverse sets 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02478 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regular clock map and trace space Gaucher, Philippe Algebraic Topology Category Theory 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 of the category of clock maps. Hence it is locally presentable. Any geometric realization of precubical sets and of transverse sets 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. |
| title | Regular clock map and trace space |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2606.02478 |