nLab
localization of model categories
Contents
Context
Model category theory
model 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
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
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
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.
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