# nLab localization of model categories

Contents

model category

## Model structures

for ∞-groupoids

### for $(\infty,1)$-sheaves / $\infty$-stacks

#### $(\infty,1)$-Category theory

(∞,1)-category theory

# Contents

## Idea

This is a notion of localization more suited to model categories. To quote Hirschhorn:

‘Localizing a model category with respect to a class of maps does not mean making the maps into isomorphisms; instead, it means making the images of those maps in the homotopy category into isomorphisms. Since the image of a map in the homotopy category is an isomorphism if and only if the map is a weak equivalence, localizing a model category with respect to a class of maps means making maps into weak equivalences.’

## References

The main classical reference is

• Hirschhorn, Localization of Model Categories (pdf)

For more references see at Bousfield localization of model categories.

Last revised on November 22, 2014 at 07:24:58. See the history of this page for a list of all contributions to it.