model category, model $\infty$-category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of $(\infty,1)$-categories
Model structures
for $\infty$-groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
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
A model category structure $M_1$ is a right Bousfield localization of a model structure $M_2$ on the same underlying category if $M_1$ and $M_2$ have the same fibrations and the weak equivalences of $M_1$ contain those of $M_2$
The notion of right Bousfield delocalization reverses this relation: $M_1$ is a right Bousfield delocalization of $M_2$ if $M_2$ is a right Bousfield localization of $M_1$.
Of course, the nontrivial task here is to establish interesting existence criteria for right Bousfield delocalizations.
If $M_1$ and $M_2$ 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 $M_3$ with the same fibrations and whose weak equivalences are the intersection of weak equivalences in $M_1$ and $M_2$. This model structure is a right Bousfield delocalization of both $M_1$ and $M_2$.
Last revised on April 23, 2015 at 18:54:46. See the history of this page for a list of all contributions to it.