Discrete homotopy hypothesis for n-types
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911462410158080 |
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| author | Carranza, Daniel Kapulkin, Chris |
| author_facet | Carranza, Daniel Kapulkin, Chris |
| contents | We show that discrete and classical homotopy theories are equivalent after localizing at n-equivalences for any non-negative integer n. By constructing an explicit homotopy inverse to the graph nerve functor associating an n-fibrant cubical set to a graph, we are also able to give explicit computations of several previously unknown discrete homotopy groups of boundaries of cubes and suspensions of cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19293 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discrete homotopy hypothesis for n-types Carranza, Daniel Kapulkin, Chris Algebraic Topology Combinatorics Category Theory Primary: 55U35, 05C10, secondary: 18N45, 18N55, 55U40 We show that discrete and classical homotopy theories are equivalent after localizing at n-equivalences for any non-negative integer n. By constructing an explicit homotopy inverse to the graph nerve functor associating an n-fibrant cubical set to a graph, we are also able to give explicit computations of several previously unknown discrete homotopy groups of boundaries of cubes and suspensions of cycles. |
| title | Discrete homotopy hypothesis for n-types |
| topic | Algebraic Topology Combinatorics Category Theory Primary: 55U35, 05C10, secondary: 18N45, 18N55, 55U40 |
| url | https://arxiv.org/abs/2602.19293 |