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
on strict ∞-categories?
symmetric monoidal (∞,1)-category of spectra
Many general results discussed at model structure on operads are based on the existence of a cocommutative Hopf interval object . In the category of chain complexes – the case for dg-operads – the Hopf interval is not cocommutative, so this case requires special discussion.
model structure on dg-operads