# nLab localization of model categories

Contents

### Context

#### Model category theory

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for $\infty$-groupoids

for ∞-groupoids

for equivariant $\infty$-groupoids

for rational $\infty$-groupoids

for rational equivariant $\infty$-groupoids

for $n$-groupoids

for $\infty$-groups

for $\infty$-algebras

general $\infty$-algebras

specific $\infty$-algebras

for stable/spectrum objects

for $(\infty,1)$-categories

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

for $(\infty,1)$-operads

for $(n,r)$-categories

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

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

(∞,1)-category theory

Background

Basic concepts

Universal constructions

Local presentation

Theorems

Extra stuff, structure, properties

Models

# 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.