### Spectra and symmetric spectra in general model categories, by Mark Hovey

This is an updated version. Following an idea of Voevodsky, we show
that all of the results of our paper apply to motivic homotopy theory.

In this paper we show that the notions of spectra and symmetric spectra
work in fairly general Quillen model categories. The most important
application is to Voevodsky's model category of sheaves in the
Nisnevitch topology, from which we can construct spectra and symmetric
spectra in order to get appropriate stable model categories whose
resulting homotopy categories are equivalent. We stress that this paper
is very general; the input from a specific model category needed to
construct spectra or symmetric spectra is minimal. We also show that,
under some hypotheses, the model categories of spectra and symmetric
spectra are Quillen equivalent. Under stronger hypotheses, which also
hold in one of the motivic settings, stable equivalences of spectra (not
symmetric spectra!) are the appropriate analogue of stable homotopy
isomorphisms.

Mark Hovey <mhovey@wesleyan.edu>