Homology, Homotopy and Applications

On left and right model categories and left and right Bousfield localizations

Clark Barwick

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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.

Article information

Homology Homotopy Appl., Volume 12, Number 2 (2010), 245-320.

First available in Project Euclid: 28 January 2011

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18G55: Homotopical algebra

Model category Bousfield localization


Barwick, Clark. On left and right model categories and left and right Bousfield localizations. Homology Homotopy Appl. 12 (2010), no. 2, 245--320. https://projecteuclid.org/euclid.hha/1296223884

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