Weak equivalences of simplicial presheaves

Mathematics – Algebraic Topology

Scientific paper

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Scientific paper

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
facts about the local homotopy theory of simplicial presheaves.

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