nLab
cellular model category

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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

  • all domain and codomain objects of elements of I are compact objects;

  • the domain objects of the elements of J are small objects relative to I;

  • the cofibrations are effective monomorphism?s.

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

Section 12 of

  • Hirschhorn, Model categories and their localizations
Revised on November 25, 2009 12:23:31 by Urs Schreiber (87.212.203.135)
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