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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Covering étendues and Freyd’s theorem
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by Kimmo I. Rosenthal PDF
Proc. Amer. Math. Soc. 99 (1987), 221-222 Request permission

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.
References
    P. Freyd, All topoi are localic, or Why permutation models prevail (unpublished typescript, Univ. of Pennsylvania, 1979).
  • Peter T. Johnstone, How general is a generalized space?, Aspects of topology, London Math. Soc. Lecture Note Ser., vol. 93, Cambridge Univ. Press, Cambridge, 1985, pp. 77–111. MR 787824
  • André Joyal and Myles Tierney, An extension of the Galois theory of Grothendieck, Mem. Amer. Math. Soc. 51 (1984), no. 309, vii+71. MR 756176, DOI 10.1090/memo/0309
  • Kimmo I. Rosenthal, Quotient systems in Grothendieck topoi, Cahiers Topologie Géom. Différentielle 23 (1982), no. 4, 425–438. MR 693508
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • 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