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math.AT2002
Weak equivalences of simplicial presheaves
Daniel Dugger, Daniel C. Isaksen
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 giv…
math.AT2002
Hypercovers and simplicial presheaves
Daniel Dugger, Sharon Hollander, Daniel C. Isaksen
We prove that Jardine's model category of simplicial presheaves can be obtained by localizing the `discrete' version at the collection of all hypercovers. One consequence is that t…