topos theory

# Contents

## Idea

For a ringed topos $\left(𝒳,𝒪\right)$ 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

Revised on March 6, 2013 19:48:40 by Zoran Škoda (161.53.130.104)