Adjoint functors and derived functors with an application to the cohomology of semigroups
Adjoint functors and derived functors with an application to the cohomology of semigroups
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伴随函子和派生函子及其在半群上同调中的应用
DOI：
10.1016/0021-8693(67)90065-8
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发表时间：
1967
影响因子：
0.9
通讯作者：
M. Rieffel
中科院分区：
文献类型：
--
作者：
W. W. Adams;M. Rieffel
在本文的第一节中，我们证明了在适当的伴随假设下，Abel范畴上某些函子的派生函子是相等的。这个定理蕴含了同调理论中的一些结果，包括Cartan-Eilenberg的“映射定理”([I]，第150页)。本文第二节给出的这一定理的主要应用是证明许多半群的上同调群(具有任意系数)与相应的小得多的子么半群的上同调群同构。这一事实被用来推广L的某些结果？L*当我们即将提交我们关于半群的工作的早期版本以供出版时，宾夕法尼亚州立大学的N·伯恩斯坦最近的论文《论半群的上同调》引起了我们的注意。本文的一些结果与我们关于半群的一些结果有相当大的重叠。
In the first section of this paper we prove that, under a suitable adjointness assumption, the derived functors of certain functors on Abelian categories are equal. This theorem implies a number of results in homology theory, including the “mapping theorem” of Cartan-Eilenberg ([I], p. 150). Our main application of this theorem, given in the second section of this paper, is to show that the cohomology groups (with arbitrary coefficients) of many semigroups are isomorphic to the corresponding cohomology groups of often much smaller submonoids. This fact is used to generalize certain results of l? l* As we were about to submit an earlier version of our work on semigroups for publication, the recent thesis of N. Bernstein at Pennsylvania State University entitled “On the Cohomology of Semigroups” was brought to our attention. Some of the results of this thesis overlap considerably with some of our results on semigroups.