Regular directed path and Moore flow
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917556705558528 |
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| author | Gaucher, Philippe |
| author_facet | Gaucher, Philippe |
| contents | 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 precubical set. The associated Moore flow gives rise to a functor from precubical sets to Moore flows which is weakly equivalent in 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00918 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Regular directed path and Moore flow Gaucher, Philippe Category Theory Algebraic Topology 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 precubical set. The associated Moore flow gives rise to a functor from precubical sets to Moore flows which is weakly equivalent in 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 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. |
| title | Regular directed path and Moore flow |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2208.00918 |