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
In a model category every morphism may be factored as a weak equivalence followed by a fibration. Specifically if the morphism is that to the terminal object, this process finds a weakly equivalent fibrant object. This is a fibrant replacement or resolution of the original object.
The dual concept is called cofibrant replacement.
If the factorization is functorial, then it yields a fibrant replacement functor. See at functorial factorization.
Last revised on February 14, 2023 at 16:29:46. See the history of this page for a list of all contributions to it.