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?
The notion of weak complicial set is a model for (the omega-nerve of) the notion of weak ∞-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
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