# nLab Verdier site

### Context

#### Topos Theory

Could not include topos theory - contents

# Contents

## Idea

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.

## Definition

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 $U \times_X U$.

## References

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