{"title":"分段空间、跨度和半分类","authors":"R. Haugseng","doi":"10.1090/proc/15197","DOIUrl":null,"url":null,"abstract":"We show that Segal spaces, and more generally category objects in an $\\infty$-category $\\mathcal{C}$, can be identified with associative algebras in the double $\\infty$-category of spans in $\\mathcal{C}$. We use this observation to prove that \"having identities\" is a property of a non-unital $(\\infty,n)$-category.","PeriodicalId":8433,"journal":{"name":"arXiv: Algebraic Topology","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Segal spaces, spans, and semicategories\",\"authors\":\"R. Haugseng\",\"doi\":\"10.1090/proc/15197\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that Segal spaces, and more generally category objects in an $\\\\infty$-category $\\\\mathcal{C}$, can be identified with associative algebras in the double $\\\\infty$-category of spans in $\\\\mathcal{C}$. We use this observation to prove that \\\"having identities\\\" is a property of a non-unital $(\\\\infty,n)$-category.\",\"PeriodicalId\":8433,\"journal\":{\"name\":\"arXiv: Algebraic Topology\",\"volume\":\"29 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Algebraic Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/proc/15197\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/proc/15197","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that Segal spaces, and more generally category objects in an $\infty$-category $\mathcal{C}$, can be identified with associative algebras in the double $\infty$-category of spans in $\mathcal{C}$. We use this observation to prove that "having identities" is a property of a non-unital $(\infty,n)$-category.
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