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Pré-Publication, Document De Travail Année : 2023

Regular directed path and Moore flow

Résumé

Using the notion of tame regular $d$-path of the topological $n$-cube, we introduce the tame regular realization of a precubical set as a multipointed $d$-space. Its execution paths correspond to the nonconstant tame regular $d$-paths in the geometric realization of the precubical set. The associated Moore flow gives rise to a functor from precubical sets to Moore flows which is weakly equivalent in the h-model structure to a colimit-preserving functor. The two functors coincide when the precubical set is spatial, and in particular proper. As a consequence, it is given a model category interpretation of the known fact that the space of tame regular $d$-paths of a precubical set is homotopy equivalent to a CW-complex. We conclude by introducing the regular realization of a precubical set as a multipointed $d$-space and with some observations about the homotopical properties of tameness.
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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

Citer

Philippe Gaucher. Regular directed path and Moore flow. 2023. ⟨hal-03741876v4⟩
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