Categories and cohomology theories
Categories and cohomology theories
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DOI：
10.1016/0040-9383(74)90022-6
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发表时间：
1974-09
期刊：
影响因子：
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通讯作者：
G. Segal
中科院分区：
文献类型：
--
作者：
G. Segal
在这篇文章中，我将描述一种将谱和上同调理论联系起来的方法，从而将上同调理论与具有适当类型的合成律的范畴联系起来。这项工作是奎伦关于代数K-理论思想的一种可能的表述，我非常感谢他向我解释这些思想。第一个是证明Barratt，Priddy和Quillen[3]，[13]将空间0F与对称群的分类空间联系起来的定理。这表明由有限集范畴产生的上同调理论(在不交并下)是稳定上同伦的。
IN THIS paper I shall describe a method of associating a spectrum, and hence a cohomology theory, to a category with a composition-law of a suitable kind. The work is one possible formulation of Quillen’s ideas about algebraic K-theory, and I am very grateful to him for explaining them to me.Two applications of the method are included. The first is to prove the theorem of Barratt, Priddy and Quillen [3],[13] relating the space 0 F to the classifying-spaces of the symmetric groups. This asserts that the cohomology theory arising from the category of finite sets (under disjoint union) is stable cohomotopy.