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Approximate maps, filter monad, and a representation of localic maps. (English) Zbl 1240.06038

Summary: A covariant representation of the category of locales by approximate maps (mimicking a natural representation of continuous maps between spaces in which one approximates points by small open sets) is constructed. It is shown that a Kleisli shape can be given, as a part of a more general Kleisli representation of meet-preserving maps. Also, we present the spectrum adjunction in this approximation setting.

MSC:

06D22 Frames, locales
18C20 Eilenberg-Moore and Kleisli constructions for monads
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