The chain replacement of a poset flow

Philippe Gaucher

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arXiv · 2607.11639

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 preserve spaces of execution paths. 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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Philippe Gaucher. 2026-07-13. The chain replacement of a poset flow. https://arxiv.org/abs/2607.11639

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