location:  Publications → journals → CMB
Abstract view

# The Verdier Hypercovering Theorem

Published:2011-05-17
Printed: Jun 2012
• J. F. Jardine,
Mathematics Department, University of Western Ontario, London, ON   N6A 5B7
 Format: LaTeX MathJax PDF

## Abstract

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: simplicial presheaf, hypercover, cocycle
 MSC Classifications: 14F35 - Homotopy theory; fundamental groups [See also 14H30] 18G30 - Simplicial sets, simplicial objects (in a category) [See also 55U10] 55U35 - Abstract and axiomatic homotopy theory