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Pré-Publication, Document De Travail Année : 2022

Regular directed path and Moore flow

Résumé

Using the notion of regular d-path of the topological n-cube, we construct the regular realization of a precubical set as a multipointed d-space. Its execution paths correspond to the tame regular d-paths of the precubical set between two vertices. By considering the associated Moore flow, we obtain a colimit-preserving functor from precubical sets to Moore flows. As a consequence, we obtain that the associated Moore flow is always m-cofibrant. This provides a model category interpretation of the known fact that the space of tame regular d-paths of a precubical set between two vertices is homotopy equivalent to a CW-complex. Finally, we prove that the flow associated with the regular realization of a precubical set coincides with the natural realization of a precubical set as a flow.
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Dates et versions

hal-03741876 , version 1 (02-08-2022)
hal-03741876 , version 2 (31-10-2022)
hal-03741876 , version 3 (14-03-2023)
hal-03741876 , version 4 (07-12-2023)
hal-03741876 , version 5 (03-01-2024)

Identifiants

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Philippe Gaucher. Regular directed path and Moore flow. 2022. ⟨hal-03741876v2⟩
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