### E_2 model structures for presheaf categories, by J.F. Jardine

[The version of the dvi file posted Oct 3 was an old one; the correct one has
been posted Oct 10.]

The paper gives E_2 model structures in the style of Dwyer-Kan-Stover
and Goerss-Hopkins for categories of simplicial objects in pointed
simplicial presheaves, presheaves of spectra and presheaves of
symmetric spectra on a small Grothendieck site. Analogs of these
results for unstable and stable motivic homotopy theory are also
displayed and proved. The key technical device is a bounded
approximation technique for objects in the respective categories,
which ultimately depends on cardinality count methods previously seen
in localization theory.

J.F. Jardine <jardine@uwo.ca>