Algebras and modules in monoidal model categories
with Stefan Schwede
One of the main motivations for defining a closed symmetric monoidal category
of spectra is to study the associated categories of ring, algebra and module
spectra. For all of the standard tools of homotopy theory to apply, Quillen
model category structures must be constructed on these associated categories.
In this paper we give general sufficient conditions for producing Quillen
model category structures on categories of rings, algebras and modules.
These conditions were created with the particular cases of symmetric spectra and
$\Gamma$-spaces in mind but also apply to many other
model categories with symmetric monoidal products. For example, they
also produce model categories on differential graded rings, algebras and