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
The notion of weak complicial set is a model for (the omega-nerve of) the notion of weak ω-category. The model structure for weak $\omega$-categories is a model category structure on the category of stratified simplicial sets, such that cofibrant-fibrant objects are precisely the weak complicial sets. This model structure may therefore be understood as a presentation of the (∞,1)-category of weak $\omega$-categories.
Section 6 of