The Left Localization Principle, completions, and cofree G-spectra

Abstract

We show under mild hypotheses that a Quillen adjunction between stable model categories induces another Quillen adjunction between their left localizations, and we provide conditions under which the localized adjunction is a Quillen equivalence. Moreover, we show that in many cases the induced Quillen equivalence is symmetric monoidal. Using our results we construct a symmetric monoidal algebraic model for rational cofree G-spectra. In the process, we also show that L-complete modules provide an abelian model for derived complete modules.