nLab
cellular model category

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Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (∞,1)-categories

Model structures

for ∞-groupoids

for ∞-groupoids

for n-groupoids

for ∞-groups

for ∞-algebras

general

specific

for stable/spectrum objects

for (∞,1)-categories

for stable (∞,1)-categories

for (∞,1)-operads

for (n,r)-categories

for (∞,1)-sheaves / ∞-stacks

Contents

Idea

A cellular model category is a particularly convenient form of a model category.

It is similar to a combinatorial model category. (For the moment, see there for more details.)

Definition

A cellular model category is a cofibrantly generated model category such that there is a set of generating cofibrations I and a set of generating acyclic cofibrations J, such that

Examples

For C a cellular model category we have that

Applications

For cellular model categories C that are left proper model categories all left Bousfield localizations L SC at any set S of morphisms are guaranteed to exist.

References

A standard textbook reference is section 12 of

  • Hirschhorn, Model categories and their localizations

In the context of algebraic model categories related discussion is in

Revised on December 10, 2011 23:06:32 by Urs Schreiber (212.87.29.231)
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