The Left Localization Principle, completions, and cofree $G$-spectra
Algebraic Topology
2021-03-16 v3 Commutative Algebra
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 -spectra. In the process, we also show that -complete modules provide an abelian model for derived complete modules.
Keywords
Cite
@article{arxiv.1910.01410,
title = {The Left Localization Principle, completions, and cofree $G$-spectra},
author = {Luca Pol and Jordan Williamson},
journal= {arXiv preprint arXiv:1910.01410},
year = {2021}
}
Comments
Revised 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