# nLab localization of model categories

model category

for ∞-groupoids

## Theorems

#### $(\infty,1)$-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.

Revised on November 22, 2014 07:24:58 by Tim Porter (2.27.157.215)