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Right delocalization of model categories

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Bruce R Corrigan-Salter

Model categories have long been a useful tool in homotopy theory, allowing
many generalizations of results in topological spaces to other categories.
Giving a localization of a model category provides an additional model
category structure on the same base category, which alters what objects
are being considered equivalent by increasing the class of weak
equivalences. In some situations, a model category where the class of
weak equivalences is restricted from the original one could be more
desirable. In this situation we need the notion of a delocalization. In
this paper, right Bousfield delocalization is defined, we provide examples
of right Bousfield delocalization as well as an existence theorem. In
particular, we show that given two model category structures $\MO$ and
$\MT$ we can define an additional model category structure $\MO \cap \MT$
by defining the class of weak equivalences to be the intersection of the
$\MO$ and $\MT$ weak equivalences. In addition we consider the model
category on diagram categories over a base category (which is endowed with
a model category structure) and show that delocalization is often
preserved by the diagram model category structure.

Keywords:
localization, delocalization, model categories, diagram

2010 MSC:
18D99, 18E35, 55P60, 18G55

*Theory and Applications of Categories,*
Vol. 31, 2016,
No. 17, pp 462-476.

Published 2016-06-09.

http://www.tac.mta.ca/tac/volumes/31/17/31-17.pdf

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