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.