Covering étendues and Freyd’s theorem

Rosenthal, Kimmo I.

doi:10.1090/S0002-9939-1987-0870775-X

Covering étendues and Freyd’s theorem
HTML articles powered by AMS MathViewer

by Kimmo I. Rosenthal

Proc. Amer. Math. Soc. 99 (1987), 221-222

DOI: https://doi.org/10.1090/S0002-9939-1987-0870775-X

PDF | 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

All topoi are localic, or Why permutation models prevail

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