Title:
Weak equivalences of simplicial presheaves

Authors:
Daniel Dugger
Daniel C. Isaksen

AMS subject classification:
55U35, 18F20

Addresses:
Department of Mathematics, Purdue University
ddugger@math.purdue.edu

Department of Mathematics, University of Notre Dame
isaksen.1@nd.edu

Abstract:

The usual way of defining weak equivalences for simplicial presheaves
is to require an isomorphism on all sheaves of homotopy groups.  We
unravel some of the machinery here, and give a more concrete
description in terms of local homotopy lifting properties.  This
characterization is used to prove some basic results about the local
homotopy theory of simplicial presheaves.