Diagram spaces, diagram spectra, and spectra of units

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This article compares the infinite loop spaces associated to symmetric spectra, orthogonal spectra, and EKMM S-modules. Each of these categories of structured spectra has a corresponding category of structured spaces that receives the infinite loop space functor Ω∞. We prove that these models for spaces are Quillen equivalent and that the infinite loop space functors Ω∞ agree. This comparison is then used to show that two different constructions of the spectrum of units gl₁ R of a commutative ring spectrum R agree.