nLab
Verdier site

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

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 UXU \to X which is part of a covering sieve on XX, also

U(Id U,Id U)U× XU U \stackrel{(Id_U,Id_U)}{\to} U \times_X U

is in a covering sieve of U× XUU \times_X U.

References

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