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 $L_0^I$-complete modules provide an abelian model for derived $I$-complete modules.

中文翻译：

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左定位原理、完成和 cofree G 谱

我们在温和的假设下表明，稳定模型类别之间的 Quillen 附属会在它们的左定位之间引发另一个 Quillen 附属，并且我们提供了局部附属是 Quillen 等价的条件。此外，我们表明，在许多情况下，诱导的 Quillen 等价是对称幺半群的。使用我们的结果，我们为有理 cofree $G$-spectra 构建了一个对称幺半群代数模型。在这个过程中，我们还展示了 $L_0^I$-complete 模块为派生的 $I$-complete 模块提供了一个阿贝尔模型。