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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Equivalences of monoidal model categories

Stefan Schwede and Brooke Shipley

Algebraic & Geometric Topology 3 (2003) 287–334

arXiv: math.AT/0209342

Abstract

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
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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