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Points in topoi of sheaves over distributive lattices
Published online by Cambridge University Press: 17 April 2009
Abstract
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This article generalizes the well known theorem that the geometric morphisms from the category of sets to a category of set-valued sheaves on a topological space correspond to the irreducible components of the topological space. As irreducible components are not available in any topos more general than a spatial one, they are characterized in terms of filters of open sets - which are available in any topos. It is then seen that the theorem phrased in these terms generalizes to sheaves on any lattice with reasonable distributivity conditions.
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- Research Article
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- Copyright © Australian Mathematical Society 1979
References
[1]Johnstone, P.T., Topos theory (London Mathematical Society Monographs, 10. Academic Press, London, New York, San Francisco, 1977).Google Scholar
[2]Mac, Saunders Lane, Categories for the working mathematician (Graduate Texts in Mathematics, 5. Springer-Verlag, New York, Heidelberg, Berlin, 1971).Google Scholar
[3]Ulmer, Friedrich, “Locally a-presentable and locally α-generated categories”, Reports of the Midwest Category Seminar V, 230–247 (Lecture Notes in Mathematics, 195. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
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