Segal space (original) (raw)
In mathematics, a Segal space is a simplicial space satisfying some pullback conditions, making it look like a homotopical version of a category. More precisely, a simplicial set, considered as a simplicial discrete space, satisfies the Segal conditions iff it is the nerve of a category. The condition for Segal spaces is a homotopical version of this. Complete Segal spaces were introduced by as models for (∞, 1)-categories.
| Property | Value |
|---|---|
| dbo:abstract | In mathematics, a Segal space is a simplicial space satisfying some pullback conditions, making it look like a homotopical version of a category. More precisely, a simplicial set, considered as a simplicial discrete space, satisfies the Segal conditions iff it is the nerve of a category. The condition for Segal spaces is a homotopical version of this. Complete Segal spaces were introduced by as models for (∞, 1)-categories. (en) |
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| dbo:wikiPageRevisionID | 950720775 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Nerve_(category_theory) dbr:Pullback dbc:Category_theory dbc:Simplicial_sets dbr:Homotopy dbr:Category_(mathematics) dbr:Simplicial_set dbr:Simplicial_space dbr:Transactions_of_the_American_Mathematical_Society dbr:(infinity,1)-category |
| dbp:id | Segal+space (en) complete+Segal+space (en) |
| dbp:title | Complete Segal space (en) Segal space (en) |
| dbp:wikiPageUsesTemplate | dbt:Citation dbt:Harvtxt dbt:Nlab |
| dcterms:subject | dbc:Category_theory dbc:Simplicial_sets |
| gold:hypernym | dbr:Space |
| rdf:type | yago:WikicatSimplicialSets yago:Abstraction100002137 yago:Collection107951464 yago:Group100031264 yago:Set107996689 |
| rdfs:comment | In mathematics, a Segal space is a simplicial space satisfying some pullback conditions, making it look like a homotopical version of a category. More precisely, a simplicial set, considered as a simplicial discrete space, satisfies the Segal conditions iff it is the nerve of a category. The condition for Segal spaces is a homotopical version of this. Complete Segal spaces were introduced by as models for (∞, 1)-categories. (en) |
| rdfs:label | Segal space (en) |
| owl:sameAs | freebase:Segal space yago-res:Segal space wikidata:Segal space https://global.dbpedia.org/id/4uvxz |
| prov:wasDerivedFrom | wikipedia-en:Segal_space?oldid=950720775&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Segal_space |
| is dbo:wikiPageDisambiguates of | dbr:Segal |
| is dbo:wikiPageRedirects of | dbr:Complete_Segal_space |
| is dbo:wikiPageWikiLink of | dbr:Glossary_of_category_theory dbr:Quasi-category dbr:Segal dbr:Siegel dbr:Complete_Segal_space |
| is foaf:primaryTopic of | wikipedia-en:Segal_space |