Model category theory
Producing new model structures
Presentation of -categories
for stable/spectrum objects
for stable -categories
for -sheaves / -stacks
Paths and cylinders
An cell complex is an object in a category which is obtained by successively “gluing cells” via pushouts.
Let be a category with colimits and equipped with a set of morphisms.
In practice is usually a cofibrantly generated model category with set of generating cofibrations and set of acyclic generating cofibrations.
An -cell complex in is an object which is connected to the initial object by a transfinite composition of pushouts of the generating cofibrations in .
A relative -cell complex (relative to any object ) is any morphism obtained this starting from .
A discussion in the context of algebraic model categories is in
Revised on December 30, 2013 00:03:00
by Tim Porter