Another approach to the Kan–Quillen model structure
By careful analysis of the embedding of a simplicial set into its image under Kan’s Ex∞ functor we obtain a new and combinatorial proof that it is a weak homotopy equivalence. Moreover, we obtain a presentation of it as a strong anodyne extension. From this description we can quickly deduce some bas...
| Main Author: | |
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| Format: | Journal article |
| Language: | English |
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Springer Nature
2019
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| _version_ | 1797061743012216832 |
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| author | Moss, S |
| author_facet | Moss, S |
| author_sort | Moss, S |
| collection | OXFORD |
| description | By careful analysis of the embedding of a simplicial set into its image under Kan’s Ex∞ functor we obtain a new and combinatorial proof that it is a weak homotopy equivalence. Moreover, we obtain a presentation of it as a strong anodyne extension. From this description we can quickly deduce some basic facts about Ex∞ and hence provide a new construction of the Kan–Quillen model structure on simplicial sets, one which avoids the use of topological spaces or minimal fibrations. |
| first_indexed | 2024-03-06T20:35:37Z |
| format | Journal article |
| id | oxford-uuid:3286eec1-ca1c-4213-a224-d20410f8b846 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:35:37Z |
| publishDate | 2019 |
| publisher | Springer Nature |
| record_format | dspace |
| spelling | oxford-uuid:3286eec1-ca1c-4213-a224-d20410f8b8462022-03-26T13:14:39ZAnother approach to the Kan–Quillen model structureJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3286eec1-ca1c-4213-a224-d20410f8b846EnglishSymplectic ElementsSpringer Nature2019Moss, SBy careful analysis of the embedding of a simplicial set into its image under Kan’s Ex∞ functor we obtain a new and combinatorial proof that it is a weak homotopy equivalence. Moreover, we obtain a presentation of it as a strong anodyne extension. From this description we can quickly deduce some basic facts about Ex∞ and hence provide a new construction of the Kan–Quillen model structure on simplicial sets, one which avoids the use of topological spaces or minimal fibrations. |
| spellingShingle | Moss, S Another approach to the Kan–Quillen model structure |
| title | Another approach to the Kan–Quillen model structure |
| title_full | Another approach to the Kan–Quillen model structure |
| title_fullStr | Another approach to the Kan–Quillen model structure |
| title_full_unstemmed | Another approach to the Kan–Quillen model structure |
| title_short | Another approach to the Kan–Quillen model structure |
| title_sort | another approach to the kan quillen model structure |
| work_keys_str_mv | AT mosss anotherapproachtothekanquillenmodelstructure |