on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
on algebras over an operad, on modules over an algebra over an operad
on dendroidal sets, for dendroidal complete Segal spaces, for dendroidal Cartesian fibrations
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.