迹范畴的余上同调
Comonad Cohomology of Track Categories
摘要：
我们定义了一个comonad上同调的轨道类别，我们表明它是由一个长的确切序列，其Dwyer-Kan-Smith上同调。在轨道范畴的温和假设下，我们证明了它的共单上同调与它的Dwyer-Kan-Smith上同调在维数移动之前是一致的，从而得到了后者的一个代数形式。我们还将我们的结果专门用于轨道类别是$2$ -广群的情况。
英文摘要：
We define a comonad cohomology of track categories and we show it is linked by a long exact sequence to its Dwyer-Kan-Smith cohomology . Under mild hypothesis on the track category, we show that its comonad cohomology coincides, up to dimension shift, with its Dwyer-Kan-Smith cohomology, therefore obtaining an algebraic formulation of the latter. We also specialize our results to the case where the track category is a $2$-groupoid.
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