Directed path and Moore flow
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914469104320512 |
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| author | Gaucher, Philippe |
| author_facet | Gaucher, Philippe |
| contents | This addendum extends prior work to the non-regular setting by introducing the tame realization of a precubical set as a multipointed $d$-space. Its execution paths are precisely the nonconstant tame $d$-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 $h$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Directed path and Moore flow Gaucher, Philippe Category Theory Algebraic Topology This addendum extends prior work to the non-regular setting by introducing the tame realization of a precubical set as a multipointed $d$-space. Its execution paths are precisely the nonconstant tame $d$-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 $h$-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. |
| title | Directed path and Moore flow |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2604.11347 |