Presheaves of symmetric spectra (Q1575027)

The main theorem of the paper [\textit{M. Hovey}, \textit{B. Shipley}, and \textit{J. Smith}, J. Am. Math. Soc. 13, No. 1, 149-208 (2000; Zbl 0931.55006)] says that there is a proper closed simplicial model category structure on the category \(\text{Spt}^\Sigma\) of symmetric spectra, and that the associated homotopy category \(\text{Ho(Spt}^\Sigma)\) is equivalent to the stable category. The paper under review shows how to generalize these results to the category \(\text{Pre Spt}^\Sigma ({\mathcal C})\) of presheaves of symmetric spectra on an arbitrary small Grothendieck site \({\mathcal C}\), this means that the category of presheaves of symmetric spectra on a small Grothendieck site \({\mathcal C}\) admits a proper closed simplicial model structure so that the associated homotopy category is adjoint equivalent to the stable category associated to presheaves of spectra on \({\mathcal C}\).