{
  "abstract": "We introduce reparametrization categories with cuts. For every such category $\\mathcal{P}$, the tensor product of two objectwise weak homotopy equivalences of $\\mathcal{P}$-spaces is an objectwise weak homotopy equivalence, and the q-model structure on $\\mathcal{P}$-flows is left proper. The reparametrization categories $\\mathcal{G}$ and $\\mathcal{M}$, as well as the terminal category $\\mathbf{1}$, 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 $\\mathbf{1}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.13165",
  "author_total": 1,
  "authors": [
    {
      "name": "Philippe Gaucher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3bg1xcvxvpeje.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.13165",
  "fulltext_url": null,
  "id": "3bg1xcvxvpeje",
  "issns": [],
  "landing_url": "https://hal.science/hal-05719472v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "math.AT"
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      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "pdf_url": "https://hal.science/hal-05719472/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3bg1xcvxvpeje.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05719472",
      "source": "hal",
      "url": "https://hal.science/hal-05719472v2"
    },
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2608.13165",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.13165"
    }
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Left properness of Moore flows",
  "title_text": "Left properness of Moore flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/3bg1xcvxvpeje",
  "venue": "HAL",
  "versions": []
}