nLab
localization of model categories
Contents
Context
Model category theory
model category , model $\infty$ -category

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

Homotopy theory
homotopy theory , (∞,1)-category theory , homotopy type theory

flavors: stable , equivariant , rational , p-adic , proper , geometric , cohesive , directed …

models: topological , simplicial , localic , …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

$(\infty,1)$ -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.’

Examples
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.