Verdier site

*Could not include topos theory - contents*

A *Verdier site* (named after Jean-Louis Verdier) is a site with an extra condition on the coverage that ensures that one can refine every hypercover in the context of simplicial presheaves on that site in a particularly nice.

For a discussion of the use of Verdier sites see descent.

A **Verdier site** is a site such that for every morphism $U \to X$ which is part of a covering sieve on $X$, also

$U \stackrel{(Id_U,Id_U)}{\to} U \times_X U$

is in a covering sieve of $U \times_X U$.

section 9 of

- Daniel Dugger, Sharon Hollander, Daniel Isaksen,
*Hypercovers and simplicial presheaves*(arXiv)

Revised on December 2, 2013 15:32:24
by David Roberts
(129.127.252.10)