Regular directed path and Moore flow

Regular directed path and Moore flow

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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 precubicalset.The associated Moore flow gives rise to a functor from precubical sets to Moore flows which is weakly equivalent in synovex one grass 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 socialstudiesscholar.com 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.