Geodesic
The Verdier Hypercovering Theorem
Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 319-328

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DOI

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.
DOI : 10.4153/CMB-2011-093-x
Mots-clés : 14F35, 18G30, 55U35, simplicial presheaf, hypercover, cocycle 
Jardine, J. F. The Verdier Hypercovering Theorem. Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 319-328. doi: 10.4153/CMB-2011-093-x
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     title = {The {Verdier} {Hypercovering} {Theorem}},
     journal = {Canadian mathematical bulletin},
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     year = {2012},
     volume = {55},
     number = {2},
     doi = {10.4153/CMB-2011-093-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-093-x/}
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