nLab
open geometric morphism

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

Contents

Idea

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

Definition

A geometric morphism

f:=(f *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)