Hypercovers and simplicial presheaves

Details Hypercovers and simplicial presheaves Hypercovers and simplicial presheaves

2002-05-02

arxiv.org/abs/math/0205027v2

Mathematics

Algebraic Topology

Revision has updated references, extra material on fibrations

Scientific paper

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 the fibrant objects can be explicitly identified in terms of a hypercover descent condition. Another is a very simple approach to change-of-site functors. In an appendix, we discuss how this hypercover localization compares to the more naive process of localizing at the Cech complexes; the two are not the same in general, but agree in some cases of interest.

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