topos theory

# Contents

## Idea

The notion of open geometric morphism is the notion of open map for geometric morphisms between toposes.

## Definition

$f:=\left({f}^{*}⊣{f}_{*}\right):ℰ\to ℱ$f := (f^* \dashv f_*) : \mathcal{E} \to \mathcal{F}

is called open if the following equivalent conditions holds

## References

• Peter Johnstone, Open maps of toposes, Manuscripta Mathematica, Volume 31, Numbers 1-3

• André Joyal, Myles Tierney, An extension of the Galois theory of Grothendieck, Mem. Amer. Math. Soc. 309 (1984).

Revised on February 13, 2012 15:58:39 by Urs Schreiber (109.144.214.106)