nLab
structure sheaf

Idea

For a ringed topos $(𝒳,𝒪)$ the ring object $𝒪\in 𝒳$ is called the structure sheaf.

More generally, for $𝒢$ a geometry (for structured (∞,1)-toposes), a structured (∞,1)-topos

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

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

In particular for $H_{\mathrm{th}}$ an

Related concepts

• sheaf of meromorphic functions

category: sheaf theory, algebraic geometry