Polynomial functors
Polynomial functors
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DOI：
10.1017/s0305004100045254
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发表时间：
1969-11
影响因子：
0.8
通讯作者：
I. B. S. Passi
中科院分区：
文献类型：
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作者：
I. B. S. Passi
1. 如果G是一个群，Z(G)是它的整群环，AG是增广理想，那么我们就可以组成阿贝尔群。在(5)中，我们研究了这些阿贝尔群的结构，我们称之为多项式群。如果C表示阿贝尔群的范畴，则Pn和Qn是从C到C的函子，我们称这些函子为多项式函子。这项工作的目的是研究这些因子的性质。除了n = 1外，这些函子都是非加性的。事实上，在Eilenberg-Maclane(4)的意义上，这些都是n次的函子（定理2·3）。由于它们的非加性，它们的衍生函子无法用传统的Cartan-Eilenberg(1)方法计算。我们必须利用最近的Dold-Puppe(3)理论。
1. Introduction: If G is a group, Z(G) its integral group-ring and AG the augmentation ideal, then we can form the Abelian groups In (5) we have studied the structure of these Abelian groups which we called polynomial grouups. If C denotes the category of Abelian groups, then Pn and Qn are functors from C into C. We call these functors polynomial functors. The object of this work is to study the nature of these funtors. Except for n = 1, these functors are non-additive. In fact, in the sense of Eilenberg–Maclane (4) these are functors of degree exactly n (Theorem 2·3). Because of their non-additive nature, their derived functors cannot be calculated in the traditional Cartan–Eilenberg(1) method. We have to make use of the more recent theory of Dold–Puppe (3).