nLab
localization of model categories

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

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

Homotopy theory

(,1)(\infty,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.’

Examples

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)