English

Directed path and Moore flow

Category Theory 2026-04-14 v1 Algebraic Topology

Abstract

This addendum extends prior work to the non-regular setting by introducing the tame realization of a precubical set as a multipointed dd-space. Its execution paths are precisely the nonconstant tame dd-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 hh-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.

Keywords

Cite

@article{arxiv.2604.11347,
  title  = {Directed path and Moore flow},
  author = {Philippe Gaucher},
  journal= {arXiv preprint arXiv:2604.11347},
  year   = {2026}
}

Comments

8 pages; addendum to arXiv:2208.00918: this note is not self-contained

R2 v1 2026-07-01T12:06:12.219Z