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A monad of valuation locales II

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If you have a question about this talk, please contact Dan Ghica.

If X is a locale then its valuation locale has for its points the valuations on X. This construction is the functor part of a strong monad on the category of locales, a localic analogue of the Giry monad. It is commutative, i.e. product valuations exist and a Fubini Theorem holds. An analogue of the Riesz Representation theorem holds. Concrete representations are given for the tensor product of lattices and for the modular monoid. The work conforms with the constructive constraints of geometric logic.

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