{"title":"Nerves and cones of free loop-free\nω-categories","authors":"Andrea Gagna, Viktoriya Ozornova, M. Rovelli","doi":"10.2140/tunis.2023.5.273","DOIUrl":null,"url":null,"abstract":"We show that the complicial nerve construction is homotopically compatible with two flavors of cone constructions when starting with an $\\omega$-category that is suitably free and loop-free. An instance of the result recovers the fact that the standard $m$-simplex is equivalent to the complicial nerve of the $m$-oriental.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tunisian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/tunis.2023.5.273","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 8
Abstract
We show that the complicial nerve construction is homotopically compatible with two flavors of cone constructions when starting with an $\omega$-category that is suitably free and loop-free. An instance of the result recovers the fact that the standard $m$-simplex is equivalent to the complicial nerve of the $m$-oriental.
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