Homotopy theory of <em>s</em>-bimodules, naive ring spectra and stable model categories

Abstract

We study the homotopy theory of S-bimodules which essentially sequential spectra which admit a left and right action of the sphere specturm in a compatible way. The resulting category has non-symmetric monoidal product. This enables us to consider non-commutative monoids in S-bimodules which we call naive ring spectra for their extremely simple structure. As application we construct naive endomorphism ring spectra for objects in a stable model category. We then prove that any compactly generated stable model category is Quillen equivalent to a category of modules over a naive ring spectrum and hence to a category of modules over a symmetric ring spectrum.