Weak equivalences of simplicial presheaves

Abstract:

The usual way to define weak equivalences of simplicial presheaves is to require an isomorphism on all sheaves of homotopy groups. In this paper we unravel some of the machinery here, and give a very concrete description in terms of local homotopy lifting properties. This characterization is used to prove some basic facts about the homotopy theory of simplicial presheaves.

• Dvi file , to appear in Proceedings of the Conference on Algebraic Topology (Evanston, 2002).