{"title":"轨道范畴的共上同调","authors":"David Blanc, Simona Paoli","doi":"10.1007/s40062-019-00235-2","DOIUrl":null,"url":null,"abstract":"<p>We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding <span>\\(({\\mathcal {S}}\\!,\\!\\mathcal {O})\\)</span>-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the <span>\\(({\\mathcal {S}}\\!,\\!\\mathcal {O})\\)</span>-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00235-2","citationCount":"1","resultStr":"{\"title\":\"Comonad cohomology of track categories\",\"authors\":\"David Blanc, Simona Paoli\",\"doi\":\"10.1007/s40062-019-00235-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding <span>\\\\(({\\\\mathcal {S}}\\\\!,\\\\!\\\\mathcal {O})\\\\)</span>-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the <span>\\\\(({\\\\mathcal {S}}\\\\!,\\\\!\\\\mathcal {O})\\\\)</span>-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2019-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40062-019-00235-2\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-019-00235-2\",\"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://link.springer.com/article/10.1007/s40062-019-00235-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding \(({\mathcal {S}}\!,\!\mathcal {O})\)-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the \(({\mathcal {S}}\!,\!\mathcal {O})\)-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.
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