nLab
right Bousfield delocalization

Contents

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

Locality and descent

Contents

Idea

A model category structure M 1M_1 is a right Bousfield localization of a model structure M 2M_2 on the same underlying category if M 1M_1 and M 2M_2 have the same fibrations and the weak equivalences of M 1M_1 contain those of M 2M_2

The notion of right Bousfield delocalization reverses this relation: M 1M_1 is a right Bousfield delocalization of M 2M_2 if M 2M_2 is a right Bousfield localization of M 1M_1.

Of course, the nontrivial task here is to establish interesting existence criteria for right Bousfield delocalizations.

Existence theorem

Theorem (Corrigan-Salter)

If M 1M_1 and M 2M_2 are two cofibrantly generated model category structures on the same category with coinciding classes of fibrations, then there is a third cofibrantly generated model structure M 3M_3 with the same fibrations and whose weak equivalences are the intersection of weak equivalences in M 1M_1 and M 2M_2. This model structure is a right Bousfield delocalization of both M 1M_1 and M 2M_2.

(Corrigan-Salter 15)

References

Last revised on April 23, 2015 at 18:54:46. See the history of this page for a list of all contributions to it.