## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Calibrated Toposes

Peter Johnstone

#### Abstract

We study a particular structure on a topos $\cal E$, related to the notion of a class of étale maps' due to Joyal and Moerdijk and to Bénabou's notion of calibration', which corresponds to giving for each object $A$ of $\cal E$ a natural' comparison between the slice category ${\cal E}/A$ and a smaller petit topos' associated with $A$. We show that there are many naturally-arising examples of such structures; but rather few of them satisfy the condition that the relation between the gros' and petit' toposes of every object is expressed by a local geometric morphism.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 5 (2012), 889-907.

Dates
First available in Project Euclid: 27 November 2012

https://projecteuclid.org/euclid.bbms/1354031555

Mathematical Reviews number (MathSciNet)
MR3009021

Zentralblatt MATH identifier
1266.18007

Subjects