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26 April 2024
 
  » arxiv » math.AT/0205027

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Hypercovers and simplicial presheaves
Daniel Dugger ; Sharon Hollander ; Daniel C. Isaksen ;
Date 2 May 2002
Subject Algebraic Topology MSC-class: 55U35,18F20 | math.AT
AbstractWe 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.
Source arXiv, math.AT/0205027
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