Contents

model category

for ∞-groupoids

# Contents

## Idea

A model category structure $M_1$ is a right Bousfield localization of a model structure $M_2$ on the same underlying category if $M_1$ and $M_2$ have the same fibrations and the weak equivalences of $M_1$ contain those of $M_2$

The notion of right Bousfield delocalization reverses this relation: $M_1$ is a right Bousfield delocalization of $M_2$ if $M_2$ is a right Bousfield localization of $M_1$.

Of course, the nontrivial task here is to establish interesting existence criteria for right Bousfield delocalizations.

## Existence theorem

###### Theorem (Corrigan-Salter)

If $M_1$ and $M_2$ are two cofibrantly generated model category structures on the same category with coinciding classes of fibrations, then there is a third cofibrantly generated model structure $M_3$ with the same fibrations and whose weak equivalences are the intersection of weak equivalences in $M_1$ and $M_2$. This model structure is a right Bousfield delocalization of both $M_1$ and $M_2$.

## References

Last revised on April 23, 2015 at 18:54:46. See the history of this page for a list of all contributions to it.