nLab localization of model categories

Contents

Context

Model category theory

Homotopy theory

$(\infty,1)$ -Category theory

Idea
Examples
References

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

localization of a simplicial model category
Bousfield localization of model categories

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.

nLab localization of model categories

Context

Model category theory

Definitions

Morphisms

Universal constructions

Producing new model structures

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

Model structures

for $\infty$ -groupoids

for equivariant $\infty$ -groupoids

for rational $\infty$ -groupoids

for rational equivariant $\infty$ -groupoids

for $n$ -groupoids

for $\infty$ -groups

for $\infty$ -algebras

general

specific

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

Homotopy theory

$(\infty,1)$ -Category theory

Background

Basic concepts

Universal constructions

Local presentation

Theorems

Extra stuff, structure, properties

Models

Contents

Idea

Examples

References

nLab localization of model categories

Context

Model category theory

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for ∞\infty-groupoids

for equivariant ∞\infty-groupoids

for rational ∞\infty-groupoids

for rational equivariant ∞\infty-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

Background

Basic concepts

Universal constructions

Local presentation

Theorems

Extra stuff, structure, properties

Models

Contents

Idea

Examples

References

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

for $\infty$ -groupoids

for equivariant $\infty$ -groupoids

for rational $\infty$ -groupoids

for rational equivariant $\infty$ -groupoids

for $n$ -groupoids

for $\infty$ -groups

for $\infty$ -algebras

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