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
Every category with limits and colimits becomes a model category by setting
the weak equivalences are the isomorphisms;
every morphism is a fibration;
every morphism is a cofibration.
This model structure regards as an (∞,1)-category with only trivial k-morphisms for .