# The Morita equivalence between parametrized spectra and module spectra

## TL;DR

This paper establishes a Quillen equivalence between parametrized spectra over BG and module spectra over an orthogonal ring spectrum, generalizing previous results and characterizing dualizable parametrized spectra.

## Contribution

It introduces an 'aggregate' model structure for diagrams of spectra indexed by a topological category and proves its Quillen equivalence to spectra over BC.

## Key findings

- Provides a complete characterization of dualizable parametrized spectra.
- Lifts several earlier results in the theory of parametrized spectra.
- Establishes a new equivalence between different models of spectra.

## Abstract

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.