Covering étendues and Freyd’s theorem
HTML articles powered by AMS MathViewer
- 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P. Freyd, All topoi are localic, or Why permutation models prevail (unpublished typescript, Univ.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
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