{"title":"关于微分等级范畴与 A 无穷范畴之间等价性的评论","authors":"James Pascaleff","doi":"10.4310/hha.2024.v26.n1.a17","DOIUrl":null,"url":null,"abstract":"We show that the homotopy theories of differential graded categories and $A_\\infty$-categories over a field are equivalent at the $(\\infty, 1)$-categorical level. The results are corollaries of a theorem of Canonaco–Ornaghi–Stellari combined with general relationships between different versions of $(\\infty, 1)$-categories.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Remarks on the equivalence between differential graded categories and A-infinity categories\",\"authors\":\"James Pascaleff\",\"doi\":\"10.4310/hha.2024.v26.n1.a17\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the homotopy theories of differential graded categories and $A_\\\\infty$-categories over a field are equivalent at the $(\\\\infty, 1)$-categorical level. The results are corollaries of a theorem of Canonaco–Ornaghi–Stellari combined with general relationships between different versions of $(\\\\infty, 1)$-categories.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/hha.2024.v26.n1.a17\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/hha.2024.v26.n1.a17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Remarks on the equivalence between differential graded categories and A-infinity categories
We show that the homotopy theories of differential graded categories and $A_\infty$-categories over a field are equivalent at the $(\infty, 1)$-categorical level. The results are corollaries of a theorem of Canonaco–Ornaghi–Stellari combined with general relationships between different versions of $(\infty, 1)$-categories.
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