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 which is part of a covering sieve on , also
is in a covering sieve of .
section 9 of
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