Homotopy $n$-types of cubical sets and graphs

Fuente: arXiv
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Main Authors: Kapulkin, Chris, Mavinkurve, Udit
Format: Preprint
Published: 2024
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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