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This article compares the infinite loop spaces associated to symmetricspectra, orthogonal spectra, and EKMM S-modules. Each of these categories ofstructured spectra has a corresponding category of structured spaces thatreceives the infinite loop space functor \Omega^\infty. We prove that thesemodels for spaces are Quillen equivalent and that the infinite loop spacefunctors \Omega^\infty agree. This comparison is then used to show that twodifferent constructions of the spectrum of units gl_1 R of a commutative ringspectrum R agree.

Diagram spaces, diagram spectra, and spectra of units