A uniqueness theorem for stable homotopy theory
A uniqueness theorem for stable homotopy theory
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稳定同伦论的唯一性定理
DOI：
10.1007/s002090100347
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发表时间：
2000
影响因子：
0.8
通讯作者：
B. Shipley
中科院分区：
文献类型：
--
作者：
S. Schwede;B. Shipley
本文研究谱的稳定同伦理论的整体结构。我们建立标准时，同伦理论与一个给定的稳定模型类别同意与经典的稳定同伦理论的谱。一个充分条件是伴随同伦范畴等价于稳定同伦范畴作为一个三角范畴，其作用是球面的稳定同伦群的环。换句话说，经典的稳定同伦理论，连同它所有的高阶信息，都是由同伦范畴作为一个三角化范畴来确定的，它具有球面的稳定同伦群的作用。另一个充分条件是存在一个小的生成对象（对应于球谱），对于这个生成对象，从无限循环空间QS ^0到自同态空间的特定“单位映射”是一个弱等价。
In this paper we study the global structure of the stable homotopy theory of spectra. We establish criteria for when the homotopy theory associated to a given stable model category agrees with the classical stable homotopy theory of spectra. One sufficient condition is that the associated homotopy category is equivalent to the stable homotopy category as a triangulated category with an action of the ring of stable homotopy groups of spheres. In other words, the classical stable homotopy theory, with all of its higher order information, is determined by the homotopy category as a triangulated category with an action of the stable homotopy groups of spheres. Another sufficient condition is the existence of a small generating object (corresponding to the sphere spectrum) for which a specific `unit map' from the infinite loop space QS^0 to the endomorphism space is a weak equivalence.