A uniqueness theorem for stable homotopy theory

Abstract

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.

Cited by in corpus (9)

• Global homotopy theory
• Brauer groups and étale cohomology in derived algebraic geometry
• Triangulated categories without models
• Group completion and units in I-spaces
• Proper equivariant stable homotopy theory
• Rigidity in Equivariant Stable Homotopy Theory
• Enhanced finite triangulated categories
• Levels of algebraicity in stable homotopy theories
• Algebraicity in monochromatic homotopy theory