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math/0205027

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Title: Hypercovers and simplicial presheaves
Authors: Daniel Dugger, Sharon Hollander, Daniel C. Isaksen
Categories: math.AT Algebraic Topology
Comments: Revision has updated references, extra material on fibrations
MSC: 55U35,18F20

Abstract: 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.

Owner: Daniel Dugger
Version 1: Thu, 2 May 2002 18:20:23 GMT
Version 2: Fri, 20 Jun 2003 22:28:38 GMT

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