{
  "abstract": "We introduce the chain replacement of a poset flow: it is obtained by considering the simplicial nerves of the posets of strictly increasing chains in the given poset, ordered by refinement. It maps posets to q-cofibrant flows and inclusions of posets to q-cofibrations. Using the combinatorial properties of the chain replacement, we prove that pushouts along the chain replacement of an order-reflecting inclusion of posets induce trivial h-cofibrations on spaces of execution paths between states of the original flow. By introducing the Hurewicz model structure on flows (or H-model structure), we deduce the same property for any q-cofibrant replacement of an order-reflecting inclusion of posets.",
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  "arxiv": "2607.11639",
  "author_total": 1,
  "authors": [
    {
      "name": "Philippe Gaucher"
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  "doi": "10.48550/arxiv.2607.11639",
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  "published": "2026-07-13",
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      "first_seen": "2026-10-30T12:17:58Z",
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      "field": "mathematics",
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    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
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  "title": "The chain replacement of a poset flow",
  "title_text": "The chain replacement of a poset flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/ed88zpxcpddg1",
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