The chain replacement of a poset flow
arXiv:2607.11639
The paper defines the chain replacement of a poset flow, converting finite posets into q‑cofibrant flows using simplicial nerves, and proves that pushouts along these replacements preserve spaces of execution paths, extending the result to the Hurewicz model structure on flows.
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 finite posets to q-cofibrant flows and inclusions of finite 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 finite 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 finite posets.
21 pages