Abstract
We give an ‘elementary’ proof, without mentioning sites, that any section of an atomic geometric morphism is open, and any section of a connected atomic morphism is an open surjection. Previously, these results were known only for bounded morphisms. As a by-product, we obtain a proof that any connected atomic morphism with a section is necessarily bounded
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References
Barr, M. and Diaconescu, R.: Atomic toposes, J. Pure Appl. Algebra 17 (1980), 1–24.
Johnstone, P. T.: Adjoint lifting theorems for categories of algebras, Bull. London Math. Soc. 7 (1975), 294–297.
Johnstone, P. T.:Topos TheoryLondon Mathematical Society Monographs No. 10, Academic Press, 1977.
Johnstone, P. T.: Open maps of toposes, Manuscripta Math. 31 (1980), 217–247.
Johnstone, P. T.: Factorization theorems for geometric morphisme, I, Cahiers Top. Géom. Diff 22 (1981), 3–17.
Joyal, A. and Tierney, M.: An Extension of the Galois Theory of GrothendieckMem. Amer. Math. Soc., 1984, p. 309.
Moerdijk, I.: The classifying topos of a continuous groupoid, I, Trans. Amer. Math. Soc. 310 (1988), 629–668.
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Dedicated to Bernhard Banaschewski, who taught me the importance of always looking for the right proof
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© 2000 Springer Science+Business Media Dordrecht
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Johnstone, P. (2000). An ‘Unsitely’ Result on Atomic Morphisms. In: Brümmer, G., Gilmour, C. (eds) Papers in Honour of Bernhard Banaschewski. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2529-3_2
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DOI: https://doi.org/10.1007/978-94-017-2529-3_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5540-8
Online ISBN: 978-94-017-2529-3
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