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：

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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。