The Morita equivalence between parametrized spectra and module spectra

We give a Quillen equivalence between May and Sigurdsson's model category of parametrized spectra over BG, and Mandell, May, Schwede, and Shipley's model category of modules over the orthogonal ring spectrum \Sigma^\infty_+ G, for each topological group G. More generally, for a topological...

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Bibliographic Details
Published in:arXiv.org 2017-09
Main Authors: Lind, John A, Malkiewich, Cary
Format: Article
Language:English
Subjects:
Equivalence
Group theory
Modules
Parameterization
Rings (mathematics)
Spectra
Topology
Online Access:Get full text
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Summary:We give a Quillen equivalence between May and Sigurdsson's model category of parametrized spectra over BG, and Mandell, May, Schwede, and Shipley's model category of modules over the orthogonal ring spectrum \Sigma^\infty_+ G, for each topological group G. More generally, for a topological category C we introduce an "aggregate" model structure on the category of diagrams of spectra indexed by C, and prove that it is Quillen equivalent to spectra over BC. This lifts several earlier results, and leads to a complete characterization of the dualizable parametrized spectra, answering a question of May and Sigurdsson.
ISSN:2331-8422