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>