Left Bousfield localization without left properness
arXiv:2001.03764 · doi:10.1016/j.jpaa.2023.107570
Abstract
Given a combinatorial (semi-)model category and a set of morphisms , we establish the existence of a semi-model category satisfying the universal property of the left Bousfield localization in the category of semi-model categories. Our main tool is a semi-model categorical version of a result of Jeff Smith, that appears to be of independent interest. Our main result allows for the localization of model categories that fail to be left proper. We give numerous examples and applications, related to the Baez-Dolan stabilization hypothesis, localizations of algebras over operads, chromatic homotopy theory, parameterized spectra, -algebras, enriched categories, dg-categories, functor calculus, and Voevodsky's work on radditive functors.
arXiv commentEdited in response to a referee report; this is the final version
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