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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Covering étendues and Freyd's theorem


Author: Kimmo I. Rosenthal
Journal: Proc. Amer. Math. Soc. 99 (1987), 221-222
MSC: Primary 18B25
DOI: https://doi.org/10.1090/S0002-9939-1987-0870775-X
MathSciNet review: 870775
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Abstract: From Freyd's covering theorem for Grothendieck topoi, it immediately follows that every Grothendieck topos $ \varepsilon $ admits a hyperconnected geometric morphism $ \mathcal{F} \to \varepsilon $, where $ \mathcal{F}$ is an étendue of (discrete) $ G$-sheaves. As a corollary, we obtain that $ \varepsilon $ admits an open surjection from a localic topos.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0870775-X
Keywords: Grothendieck topos, étendue, localic topos
Article copyright: © Copyright 1987 American Mathematical Society