Abstract

. The classical infinite loopspace machines in fact induce an equivalence of categories between a localization of the category of symmetric monoidal categories and the stable homotopy category of-1-connective spectra. Introduction Since the early seventies it has been known that the classifying spaces of small symmetric monoidal categories are infinite loop spaces, the zeroth space in a spectrum, a sequence of spaces X i ; i 0 with given homotopy equivalences to the loops on the succeeding space X i \Gamma!\Omega X i+1 . Indeed, many of the classical examples of infinite loop spaces were found as such classifying spaces ( e.g. [Ma2], [Se]). These infinite loop spaces and spectra are of great interest to topologists. The homotopy category formed by inverting the weak equivalences of spectra is the stable homotopy category, much better behaved than but still closely related to the usual homotopy category of spaces (e.g., [Ad] III ). One has in fact classically a functor Spt from t...

Citations