论文标题
通过免费的动作线性类别和应用程序应用程序解决Hochschild-Mitchell（CO）同源性解决
Resolving by a free action linear category and applications to Hochschild-Mitchell (co)homology
论文作者
论文摘要
让$ g $是一个在field $ k $上的小型类别$ \ mathcal c $上作用的集团，即$ \ mathcal c $是$ g $ - $ k $ -scategory。我们首先获得$ \ Mathcal c $可以通过$ g $ - $ k $ - 等效的类别来解决，在该类别上，$ g $在其上自由作用于对象。 这种解析类别使得能够表明，如果共同变量和不变的函数是准确的，那么$ \ Mathcal c $的Hochschild-Mitchell（CO）同源性的共同变量和不变式是对Hochschild-Mitchell（Co）的微不足道的组成部分。 c [g] $。否则，相应的频谱序列就可以解决。 如果$ g $的操作在对象上是免费的，则可以在商类别的商类别$ \ Mathcal c/g $的同源性沿$ g $的$ g $的类别中进行典范分解。这样，我们提供了一般框架的单态性框架，该框架先前以低度描述。
Let $G$ be a group acting on a small category $\mathcal C$ over a field $k$, that is $\mathcal C$ is a $G$-$k$-category. We first obtain that $\mathcal C$ is resolvable by a category which is $G$-$k$-equivalent to it, on which $G$ acts freely on objects. This resolvent category enables to show that if the coinvariants and the invariants functors are exact, then the coinvariants and invariants of the Hochschild-Mitchell (co)homology of $\mathcal C$ are isomorphic to the trivial component of the Hochschild-Mitchell (co)ho\-mo\-logy of the skew category $\mathcal C[G]$. Otherwise the corresponding spectral sequence can be settled. If the action of $G$ is free on objects, there is a canonical decomposition of the Hochschild-Mitchell (co)homology of the quotient category $\mathcal C/G$ along the conjugacy classes of $G$. This way we provide a general frame for monomorphisms which have been described previously in low degrees.
