Homotopy $n$-types of cubical sets and graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908723770818560 |
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| author | Kapulkin, Chris Mavinkurve, Udit |
| author_facet | Kapulkin, Chris Mavinkurve, Udit |
| contents | We give a new construction of the model structure on the category of simplicial sets for homotopy $n$-types, originally due to Elvira-Donazar and Hernandez-Paricio, using a right transfer along the coskeleton functor. We observe that an analogous model structure can be constructed on the category of cubical sets, and use it to equip the category of (simple) graphs with a fibration category structure whose weak equivalences are discrete $n$-equivalences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homotopy $n$-types of cubical sets and graphs Kapulkin, Chris Mavinkurve, Udit Category Theory Algebraic Topology Combinatorics 18N45, 05C25 (primary), 18N40, 55U35 (secondary) We give a new construction of the model structure on the category of simplicial sets for homotopy $n$-types, originally due to Elvira-Donazar and Hernandez-Paricio, using a right transfer along the coskeleton functor. We observe that an analogous model structure can be constructed on the category of cubical sets, and use it to equip the category of (simple) graphs with a fibration category structure whose weak equivalences are discrete $n$-equivalences. |
| title | Homotopy $n$-types of cubical sets and graphs |
| topic | Category Theory Algebraic Topology Combinatorics 18N45, 05C25 (primary), 18N40, 55U35 (secondary) |
| url | https://arxiv.org/abs/2408.05289 |