Equivalences of monoidal model categories

Schwede, Stefan¹ ; Shipley, Brooke²

¹SFB 478 Geometrische Strukturen in der Mathematik, Westfälische Wilhelms-Universität, Münster, Germany
²Department of Mathematics, Purdue University, W. Lafayette, IN 47907, USA

Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 287-334

Résumé

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.

Détail

DOI : 10.2140/agt.2003.3.287

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

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