On left and right model categories and left and right Bousfield localizations
We verify the existence of left Bousfield localizations and of enriched left Bousfield localizations, and we prove a collection of useful technical results characterizing certain fibrations of (enriched) left Bousfield localizations. We also use such Bousfield localizations to construct a number of...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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International Press of Boston, Inc.
2013
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| Online Access: | http://hdl.handle.net/1721.1/79847 |
| _version_ | 1826196444850159616 |
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| author | Barwick, Clark Edward |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Barwick, Clark Edward |
| author_sort | Barwick, Clark Edward |
| collection | MIT |
| description | We verify the existence of left Bousfield localizations and of enriched left Bousfield localizations, and we prove a collection of useful technical results characterizing certain fibrations of (enriched) left Bousfield localizations. We also use such Bousfield localizations to construct a number of new model categories, including models for the homotopy limit of right Quillen presheaves, for Postnikov towers in model categories, and for presheaves valued in a symmetric monoidal model category satisfying a homotopy-coherent descent condition. We then verify the existence of right Bousfield localizations of right model categories, and we apply this to construct a model of the homotopy limit of a left Quillen presheaf as a right model category. |
| first_indexed | 2024-09-23T10:26:38Z |
| format | Article |
| id | mit-1721.1/79847 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:26:38Z |
| publishDate | 2013 |
| publisher | International Press of Boston, Inc. |
| record_format | dspace |
| spelling | mit-1721.1/798472022-09-30T21:11:23Z On left and right model categories and left and right Bousfield localizations Barwick, Clark Edward Massachusetts Institute of Technology. Department of Mathematics Barwick, Clark Edward We verify the existence of left Bousfield localizations and of enriched left Bousfield localizations, and we prove a collection of useful technical results characterizing certain fibrations of (enriched) left Bousfield localizations. We also use such Bousfield localizations to construct a number of new model categories, including models for the homotopy limit of right Quillen presheaves, for Postnikov towers in model categories, and for presheaves valued in a symmetric monoidal model category satisfying a homotopy-coherent descent condition. We then verify the existence of right Bousfield localizations of right model categories, and we apply this to construct a model of the homotopy limit of a left Quillen presheaf as a right model category. 2013-08-14T13:21:43Z 2013-08-14T13:21:43Z 2010-11 2009-07 Article http://purl.org/eprint/type/JournalArticle 1532-0073 1532-0081 http://hdl.handle.net/1721.1/79847 Barwick, Clark. "On Left and Right Model Categories and Left and Right Bousfield Localizations." Homology, Homotopy and Applications 12(2) (2010): 245-320. en_US http://intlpress.com/HHA/v12/n2/a9/v12n2a9.pdf Homology Homotopy and Applications Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf International Press of Boston, Inc. MIT web domain |
| spellingShingle | Barwick, Clark Edward On left and right model categories and left and right Bousfield localizations |
| title | On left and right model categories and left and right Bousfield localizations |
| title_full | On left and right model categories and left and right Bousfield localizations |
| title_fullStr | On left and right model categories and left and right Bousfield localizations |
| title_full_unstemmed | On left and right model categories and left and right Bousfield localizations |
| title_short | On left and right model categories and left and right Bousfield localizations |
| title_sort | on left and right model categories and left and right bousfield localizations |
| url | http://hdl.handle.net/1721.1/79847 |
| work_keys_str_mv | AT barwickclarkedward onleftandrightmodelcategoriesandleftandrightbousfieldlocalizations |