model category, model -category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of -categories
Model structures
for -groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
for equivariant -groupoids
for rational -groupoids
for rational equivariant -groupoids
for -groupoids
for -groups
for -algebras
general -algebras
specific -algebras
for stable/spectrum objects
for -categories
for stable -categories
for -operads
for -categories
for -sheaves / -stacks
The classical model category structure on pointed topological spaces is the model structure on pointed objects of the classical model structure on topological spaces under the point (a pointed model category).
Equipped with the smash product this is a monoidal model category.
Recall that the generatic cofibrations of the classical model structure on topological spaces are
and the generating acylic cofibrations are
Write
for the operation of freely adjoining a basepoint.
The coslice model structure is itself cofibrantly generated, with generating cofibrations
and generating acyclic cofibrations
This is a special case of a general statement about cofibrant generation of coslice model structures, see this proposition.
Textbook accounts:
Last revised on July 20, 2021 at 10:34:56. See the history of this page for a list of all contributions to it.