# nLab structure sheaf

### Context

#### Topos Theory

Could not include topos theory - contents

# Contents

## Idea

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

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

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

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

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

## References

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