We construct 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 [Algebras and modules in monoidal
model categories, Proc. London Math. Soc. 80 (2000), 491–511]. 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, Topology, 42 (2003) 103–153] concerning stable model categories
translate to any one of the known symmetric monoidal model categories of
spectra.
Keywords
model category, monoidal category, Dold–Kan equivalence,
spectra
