A monad of valuation locales
نویسنده
چکیده
If X is a locale then its valuation locale VX has for its points the valuations on X. V 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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