  An n-truncated model structure on simplicial (pre-)sheaves is described
having as weak equivalences maps that induce isomorphisms on certain homotopy
sheaves only up to degree n. Starting from one of Jardine's intermediate model
structures we construct such an n-type model structure via
Bousfield-Friedlander localization and exhibit useful generating sets of
trivial cofibrations. Injectively fibrant objects in these categories are
called n-hyperstacks. The whole setup can consequently be viewed as a
description of the homotopy theory of higher hyperstacks. More importantly, we
construct analogous n-truncations on simplicial groupoids and prove a Quillen
equivalence between these settings. We achieve a classification of n-types of
simplicial presheaves in terms of (n-1)-types of presheaves of simplicial
groupoids. Our classification holds for general n. Therefore this can also be
viewed as the homotopy theory of (pre-)sheaves of (weak) higher groupoids.
