三次分解与导出函子

摘要：

我们在任意范畴中引入了具有伪连接的伪立方对象，通过适当放松它们的身份，从具有连接的立方对象的Brown-Higgins结构中获得，并构造了一个Tierney-Vogel单纯导出函子理论的立方模拟。在构造中的关键点是，射影预三次分解，自然地用来定义我们的三次导出函子具有伪退化和伪联络。同样的事实本质上是用来证明的情况下，一个加法函阿贝尔范畴之间的交换范畴，我们的理论符合经典的相对理论的导出函子的Eilenberg-Moore。

英文摘要：

We introduce pseudocubical objects with pseudoconnections in an arbitrary category, obtained from the Brown-Higgins structure of a cubical object with connections by suitably relaxing their identities, and construct a cubical analog of the Tierney-Vogel theory of simplicial derived functors. The crucial point in the construction is that projective precubical resolutions which are naturally used to define our cubical derived functors possess pseudodegeneracies and pseudoconnections. The same fact is essentially used for proving that in the case of an additive functor between abelian categories, our theory coincides with the classical relative theory of derived functors by Eilenberg-Moore.

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