with Mark Hovey and Jeff Smith
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.