cellular model category
Model category theory
Producing new model structures
Presentation of -categories
for stable/spectrum objects
for stable -categories
for -sheaves / -stacks
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.)
A cellular model category is a cofibrantly generated model category such that there is a set of generating cofibrations and a set of generating acyclic cofibrations , such that
all domain and codomain objects of elements of are compact objects relative to (in the sense of Hirschhorn);
the domain objects of the elements of are small objects relative to ;
the cofibrations are effective monomorphisms.
For a cellular model category we have that
For cellular model categories that are left proper model categories all left Bousfield localizations at any set of morphisms are guaranteed to exist.
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 March 9, 2016 16:27:46
by Urs Schreiber