  Given a small simplicial category $\C$ whose underlying ordinary category is
equipped with a Grothendieck topology $\tau$, we construct a model structure on
the category of simplicially enriched presheaves on $\C$ where the weak
equivalences are the local weak equivalences of the underlying (non-enriched)
simplicial presheaves. We show that this model category is a $t$-complete model
topos and describe the Grothendieck topology $[\tau]$ on the homotopy category
of $\C$ that corresponds to this model topos. After we first review a proof
showing that the motivic homotopy theory is not a model topos, we specialize
this construction to the category of smooth schemes of finite type, which is
simplicially enriched using the standard algebraic cosimplicial object, and
compare the result with the motivic homotopy theory. We also collect some
partial positive results on the exactness properties of the motivic
localization functor.
