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Proceedings of the American Mathematical Society

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Covering étendues and Freyd's theorem


Author: Kimmo I. Rosenthal
Journal: Proc. Amer. Math. Soc. 99 (1987), 221-222
MSC: Primary 18B25
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.


References [Enhancements On Off] (What's this?)

  • [1] P. Freyd, All topoi are localic, or Why permutation models prevail (unpublished typescript, Univ. of Pennsylvania, 1979).
  • [2] 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
  • [3] 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, 10.1090/memo/0309
  • [4] 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

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