Directed paths and Moore flows
arXiv:2604.11347
The paper introduces a tame realization of a precubical set as a multipointed d‑space, identifies its execution paths with non‑constant tame directed paths, and constructs a functor to Moore flows that is weakly equivalent to a colimit‑preserving functor within the h‑model structure.
Abstract
This addendum extends prior work to the non-regular setting by introducing the tame realization of a precubical set as a multipointed -space. Its execution paths are precisely the nonconstant tame -paths in the geometric realization of the precubical set. The associated Moore flow induces a functor from precubical sets to Moore flows, which is naturally weakly equivalent, within the -model structure, to a colimit-preserving functor whose image is included in the class of m-cofibrant Moore flows. For spatial (and thus proper) precubical sets, these functors coincide.
8 pages; addendum to arXiv:2208.00918: this note is not self-contained