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.

arXiv commentRevised version, to appear in J. Pure Appl. Algebra. v3: corrigendum added as an appendix, together with footnotes in the main body directing the reader to the corrigendum where necessary

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Cited by in corpus (5)

• The Left Localization Principle, completions, and cofree $G$-spectra
• An introduction to algebraic models for rational G-spectra
• The homotopy theory of complete modules
• Algebraic models of change of groups functors in (co)free rational equivariant spectra
• Flatness and Shipley's algebraicization theorem