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
A model category structure on presheaves of spectra presents the stabilization of the corresponding (∞,1)-category presented by the corresponding model structure on simplicial presheaves.
Over the trivial site it reproduces the model structure on spectra themselves.