关于某些复合函子的幂等性

比较左和右导出函子的复合

Comparing composites of left and right derived functors

我们引入了一个新的范畴框架研究导出函子，特别是比较复合材料的左，右导出函子。我们的中心观察是，模型范畴是一个双范畴的对象，其垂直和水平箭头分别是左和右Quillen函子，并且到导出函子的通路在这个双范畴的水平上是函子的。双范畴中的合取与配对理论是对双范畴中的合取与配对理论的推广，它给出了比较左、右导出函子复合的规范方法。我们给出了一些示例应用程序，其中大部分是改进现有的文献中的证明。

关于Singer函子R_1和Fix函子

On the Singer functor R_1 and the functor Fix

利用Lannes的T-函子构造了Steenrod代数A上不稳定模范畴U上的Singer函子R_1。这就直接证明了复合函子Fix R_1与恒等式自然等价。进一步推导了函子R_1的性质，特别是当应用于约化和零闭不稳定模时。

Dimension quotients, Fox subgroups and limits of functors

This paper presents a description of the fourth dimension quotient, using the theory of limits of functors from the category of free presentations of a given group to the category of abelian groups. A functorial description of a quotient of the third Fox subgroup is given and, as a consequence, an identification (not involving an isolator) of the third Fox subgroup is obtained. It is shown that the limit over the category of free representations of the third Fox quotient represents the composite of two derived quadratic functors.