Open Access
december 2012 Calibrated Toposes
Peter Johnstone
Bull. Belg. Math. Soc. Simon Stevin 19(5): 889-907 (december 2012). DOI: 10.36045/bbms/1354031555


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.


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Peter Johnstone. "Calibrated Toposes." Bull. Belg. Math. Soc. Simon Stevin 19 (5) 889 - 907, december 2012.


Published: december 2012
First available in Project Euclid: 27 November 2012

zbMATH: 1266.18007
MathSciNet: MR3009021
Digital Object Identifier: 10.36045/bbms/1354031555

Primary: 18B25

Keywords: Calibration , local morphism , locally connected morphism , topos

Rights: Copyright © 2012 The Belgian Mathematical Society

Vol.19 • No. 5 • december 2012
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