Open Access
2003 Equivalences of monoidal model categories
Stefan Schwede, Brooke Shipley
Algebr. Geom. Topol. 3(1): 287-334 (2003). DOI: 10.2140/agt.2003.3.287


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.


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Stefan Schwede. Brooke Shipley. "Equivalences of monoidal model categories." Algebr. Geom. Topol. 3 (1) 287 - 334, 2003.


Received: 18 August 2002; Revised: 11 February 2003; Accepted: 11 March 2003; Published: 2003
First available in Project Euclid: 21 December 2017

MathSciNet: MR1997322
zbMATH: 1028.55013
Digital Object Identifier: 10.2140/agt.2003.3.287

Primary: 55U35
Secondary: 18D10 , 55P43 , 55P62

Keywords: Dold–Kan equivalence , model category , monoidal category , spectra

Rights: Copyright © 2003 Mathematical Sciences Publishers

Vol.3 • No. 1 • 2003
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