Right Bousfield localizations (alias **cellularizations**) of model categories are a way to encode coreflective localizations of (∞,1)-categories in the setting of model categories.

Given a model category $M$, the formal definition and elementary properties can be deduced from the definition and properties of left Bousfield localizations of the opposite category of $M$.

However, the typical existence theorems for right Bousfield localizations are not formulated in this manner, since typical conditions involve some form of local presentability? of the underlying category, or an analogous condition, which typically do not hold for the opposite category.

If $C$ is a tractable model category, $D$ is an accessible accessibly embedded subcategory of $C$ that is closed under homotopy colimits in $C$. Then there is a right Bousfield localization of $C$, which is a right model category? (but not necessarily a model category), and its colocal objects are precisely the object of $D$.

The original article:

- A. K. Bousfield,
*The localization of spaces with respect to homology*, Topology**14**(1975), 133–150 [doi:10.1016/0040-9383(75)90023-3]

Detailed discussion (including existence results for left proper cellular model categories):

- Philip Hirschhorn, Chapter 5 of:
*Model Categories and Their Localizations*, AMS Math. Survey and Monographs 99 (2002) [ISBN:978-0-8218-4917-0, pdf toc, pdf]

Existence results for combinatorial model categories:

- Clark Barwick,
*On left and right model categories and left and right Bousfield localizations*, Homology, Homotopy and Applications**12**2 (2010) 245–320 [doi:10.4310/hha.2010.v12.n2.a9, euclid:1296223884, subsuming: arXiv:0708.2067, arXiv:0708.2832, arXiv:0708.3435]

Right Bousfield localization specifically for stable model categories (such as model structures on spectra):

- D. Barnes and C. Roitzheim. Stable left and right Bousfield localisations. Glasg. Math. J., 56(1):13–42, 2014.

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Created on December 28, 2023 at 22:11:22. See the history of this page for a list of all contributions to it.