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PreprintCC BY 4.0HAL

Left properness of Moore flows

  • Philippe Gaucher
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Abstract

We introduce reparametrization categories with cuts. For every such category 𝒫, the tensor product of two objectwise weak homotopy equivalences of 𝒫-spaces is an objectwise weak homotopy equivalence, and the q-model structure on 𝒫-flows is left proper. The reparametrization categories 𝒢 and ℳ, as well as the terminal category 1, have cuts. The terminal category recovers the left properness of the q-model structure on ordinary flows. We also give a symmetric reparametrization category with cuts and a strict unit. This category is not equivalent to 1.

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Cite

BibTeXRIS
BibTeX
@misc{gaucher2026left,
  title = {{Left properness of Moore flows}},
  author = {Philippe Gaucher},
  howpublished = {HAL},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.13165},
  eprint = {2608.13165},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05719472v2},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Left properness of Moore flows
AU  - Philippe Gaucher
PY  - 2026
DA  - 2026/08/17
PB  - HAL
DO  - 10.48550/arxiv.2608.13165
UR  - https://hal.science/hal-05719472v2
AB  - We introduce reparametrization categories with cuts. For every such category 𝒫, the tensor product of two objectwise weak homotopy equivalences of 𝒫-spaces is an objectwise weak homotopy equivalence, and the q-model structure on 𝒫-flows is left proper. The reparametrization categories 𝒢 and ℳ, as well as the terminal category 1, have cuts. The terminal category recovers the left properness of the q-model structure on ordinary flows. We also give a symmetric reparametrization category with cuts and a strict unit. This category is not equivalent to 1.
ER  -