Equivalences of monoidal model categories

with Stefan Schwede

ABSTRACT. We show that there are Quillen equivalences between the model categories of monoids (rings), modules and algebras over two Quillen equivalent model categories under certain conditions. This is a continuation of our earlier work where we established model categories of monoids, modules and algebras in Algebras and modules in monoidal model categories. As an application we extend the Dold-Kan equivalence to show that the model categories of simplicial rings, modules and algebras are Quillen equivalent to the associated model categories of connected differential graded rings, modules and algebras. We also show that our classification results from Stable model categories are categories of modules translate to any one of the known symmetric monoidal model categories of spectra.