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The chain replacement of a poset flow

  • Philippe Gaucher
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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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Cite

BibTeXRIS
BibTeX
@misc{gaucher2026chain,
  title = {{The chain replacement of a poset flow}},
  author = {Philippe Gaucher},
  howpublished = {HAL},
  year = {2026},
  month = jul,
  doi = {10.48550/arxiv.2607.11639},
  eprint = {2607.11639},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05691574v3},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The chain replacement of a poset flow
AU  - Philippe Gaucher
PY  - 2026
DA  - 2026/07/13
PB  - HAL
DO  - 10.48550/arxiv.2607.11639
UR  - https://hal.science/hal-05691574v3
AB  - 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.
ER  -