Homology, Homotopy and Applications

Volume 12 (2010)

Number 2

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

Pages: 245 – 320

DOI: https://dx.doi.org/10.4310/HHA.2010.v12.n2.a9


Clark Barwick (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


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.


model category, Bousfield localization

2010 Mathematics Subject Classification


Published 1 January 2010