Left Bousfield localization without left properness
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866929347093331968 |
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| author | White, David Batanin, Michael |
| author_facet | White, David Batanin, Michael |
| contents | Given a combinatorial (semi-)model category $M$ and a set of morphisms $C$, we establish the existence of a semi-model category $L_C M$ 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, $C^*$-algebras, enriched categories, dg-categories, functor calculus, and Voevodsky's work on radditive functors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_03764 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Left Bousfield localization without left properness White, David Batanin, Michael Algebraic Topology Category Theory Given a combinatorial (semi-)model category $M$ and a set of morphisms $C$, we establish the existence of a semi-model category $L_C M$ 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, $C^*$-algebras, enriched categories, dg-categories, functor calculus, and Voevodsky's work on radditive functors. |
| title | Left Bousfield localization without left properness |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2001.03764 |