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Comonad cohomology of track categories
Journal of Homotopy and Related Structures ( IF 0.7 ) Pub Date : 2019-05-14 , DOI: 10.1007/s40062-019-00235-2
David Blanc , Simona Paoli

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.

中文翻译:

轨道类别的Comonad同调

我们定义了轨道类别的共谐同调,并表明它通过一个较长的精确序列与对应的\(({mathcal {S}} \!,\!\\ mathcal {O})\)-同调性相关。在温和的假设下,直到重新索引为止,共通同调与\(({\ mathcal {S}} \!,\!\!\ mathcal {O})\)-同调重合,产生了后者的代数描述。我们还专门处理轨道类别为2群的情况。
更新日期:2019-05-14
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