### Weak equivalences of simplicial presheaves, by Daniel Dugger and Daniel C. Isaksen

Weak equivalences of simplicial presheaves are usually defined in
terms of sheaves of homotopy groups. We give another characterization
using relative-homotopy-liftings, and develop the tools necessary to
prove that this agrees with the usual definition. From our lifting
criteria we are able to prove some foundational (but new) results about
the local homotopy theory of simplicial presheaves.

Daniel Dugger <ddugger@math.purdue.edu>

Daniel C. Isaksen <isaksen.1@nd.edu>