Algebraic and Geometric Topology 3 (2003), paper no. 11, pages 287-334.

Equivalences of monoidal model categories

Stefan Schwede, Brooke Shipley

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

AMS subject classification. Primary: 55U35. Secondary: 18D10, 55P43, 55P62.

DOI: 10.2140/agt.2003.3.287

E-print: arXiv:math.AT/0209342

Submitted: 18 August 2002. (Revised: 11 February 2003.) Accepted: 11 March 2003. Published: 13 March 2003.

Notes on file formats

Stefan Schwede, Brooke Shipley
SFB 478 Geometrische Strukturen in der Mathematik
Westfaelische Wilhelms-Universitaet Muenster, Germany
Department of Mathematics, Purdue University
W. Lafayette, IN 47907, USA


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