nLab
structure sheaf

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

Higher geometry

Contents

Idea

For a ringed topos (𝒳,𝒪)(\mathcal{X}, \mathcal{O}) the ring object 𝒪𝒳\mathcal{O} \in \mathcal{X} is called the structure sheaf.

More generally, for 𝒢\mathcal{G} a geometry (for structured (∞,1)-toposes), a structured (∞,1)-topos

𝒪:𝒢𝒳 \mathcal{O} : \mathcal{G} \to \mathcal{X}

is an (∞,1)-topos equipped with a 𝒢\mathcal{G}-valued structure sheaf presented by the finite-limits-preserving and cover-preserving (∞,1)-functor 𝒪\mathcal{O}.

References

Revised on February 19, 2018 23:15:10 by Urs Schreiber (195.229.110.1)