Equivalences of monoidal model categories

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

Mathematical Subject Classification 2000

Primary: 55U35

Secondary: 18D10, 55P43, 55P62

References

Forward citations

Publication

Received: 18 August 2002

Revised: 11 February 2003

Accepted: 11 March 2003

Published: 13 March 2003

Authors

Stefan Schwede
SFB 478 Geometrische Strukturen in der Mathematik Westfälische Wilhelms-Universität Münster Germany

Brooke Shipley
Department of Mathematics Purdue University W. Lafayette, IN 47907 USA

Volume 3, issue 1 (2003)

Stefan Schwede and Brooke Shipley