Bulletin of the Belgian Mathematical Society - Simon Stevin

Calibrated Toposes

Peter Johnstone

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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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1354031555

Mathematical Reviews number (MathSciNet)
MR3009021

Zentralblatt MATH identifier
1266.18007

Subjects
Primary: 18B25: Topoi [See also 03G30]

Keywords
Topos calibration locally connected morphism local morphism

Citation

Johnstone, Peter. Calibrated Toposes. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 5, 889--907. https://projecteuclid.org/euclid.bbms/1354031555


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