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>