Stabilization as a CW approximation Original Research Article

This paper describes a peculiar property of the category of S-modules constructed by the author, Kriz, Mandell, and May: the full subcategory of suspension spectra (all of which are S-modules) forms a precise copy of the category of topological spaces. Consequently, the “classical” homotopy category of S-modules with morphisms the actual homotopy classes of maps contains a copy of unstable homotopy theory. Stabilization and stable homotopy are induced by CW approximation as S-modules. One consequence is that CW complexes whose suspension spectra are CW S-modules must be contractible.