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
symmetric monoidal (∞,1)-category of spectra
A model category structue on (commutative) monoids in a symmetric monoidal category of spectra which serves to present the homotopy theory of A-∞ rings/E-∞ rings.
Constructions modeled on symmetric ring spectra include
Michael Mandell, Peter May, Stefan Schwede, Brooke Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001), (KTheory:0320)
Brooke Shipley, A convenient model category for commutative ring spectra, Contemporary Mathematics, Volume 346, 2004
Stefan Schwede, chapter III.6 of Symmetric spectra, 2012 (pdf)