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The Verdier Hypercovering Theorem

Published online by Cambridge University Press:  20 November 2018

J. F. Jardine
J. F. Jardine*
Affiliation:
Mathematics Department, University of Western Ontario, London, ON N6A 5B7e-mail: jardine@uwo.ca
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Abstract

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This note gives a simple cocycle-theoretic proof of the Verdier hypercovering theorem. This theorem approximates morphisms $[X,\,Y]$ in the homotopy category of simplicial sheaves or presheaves by simplicial homotopy classes of maps, in the case where $Y$ is locally fibrant. The statement proved in this paper is a generalization of the standard Verdier hypercovering result in that it is pointed (in a very broad sense) and there is no requirement for the source object $X$ to be locally fibrant.

Keywords

14F3518G3055U35simplicial presheafhypercovercocycle
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 2 , 01 June 2012 , pp. 319 - 328
Copyright
Copyright © Canadian Mathematical Society 2012

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