论文标题
同源性理论在两种共同霍普夫代数的类别中有价值
Homology theory valued in the category of bicommutative Hopf algebras
论文作者
论文摘要
广义同源性理论的代码类别类别是环上模块的类别。对于A类别A，A值（广义）同源性理论是通过正式替换模块类别的定义。表示H。在本文中，我们提供了一些构建H值同源理论的方法。作为主要结果，我们给出了H值同源理论，其系数既不是组Hopf代数也不是Hopf代数。这些示例不仅包含普通同源性理论，还包含非凡理论。
The codomain category of a generalized homology theory is the category of modules over a ring. For an abelian category A, an A-valued (generalized) homology theory is defined by formally replacing the category of modules with the category A. It is known that the category of bicommutative (i.e. commutative and cocommutative) Hopf algebras over a field k is an abelian category. Denote the category by H. In this paper, we give some ways to construct H-valued homology theories. As a main result, we give H-valued homology theories whose coefficients are neither group Hopf algebras nor function Hopf algebras. The examples contain not only ordinary homology theories but also extraordinary ones.
