nLab fibrant replacement



Model category theory

model category, model \infty -category



Universal constructions


Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for equivariant \infty-groupoids

for rational \infty-groupoids

for rational equivariant \infty-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general \infty-algebras

specific \infty-algebras

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\infty,1)-sheaves / \infty-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.