nLab
structure sheaf

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}.

In particular for H th\mathbf{H}_{th} an

References

Revised on July 3, 2014 06:15:58 by Urs Schreiber (92.68.97.89)