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Points in topoi of sheaves over distributive lattices

Published online by Cambridge University Press:  17 April 2009

M. Adelman
M. Adelman
Affiliation:
School of Mathematics and Physics, Macquarie University, North Ryde, New South Wales.
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 2 , April 1979 , pp. 273 - 279
Copyright
Copyright © Australian Mathematical Society 1979

References

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