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 -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.
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