Symmetric spectra

with Mark Hovey and Jeff Smith

ABSTRACT. The stable homotopy category of spectra, much studied by algebraic topologists, is a closed symmetric monoidal category (or a category with a tensor product). For many years, however, there has been no well-behaved closed symmetric monoidal category of spectra whose homotopy category is the stable homotopy category. In this paper, we present such a category of spectra: the category of symmetric spectra. The category of symmetric spectra has a combinatorial construction which allows application to different settings, e.g. Jardine's work on the stable motivic homotopy theory of Voevodsky, and generalizes to define the diagram spectra mentioned below.