{"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}
引用次数: 1
Abstract
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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