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Approximate maps, filter monad, and a representation of localic maps

Bernhard BanaschewskiAleš Pultr — 2010

Archivum Mathematicum

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 it can be given a Kleisli shape, as a part of a more general Kleisli representation of meet preserving maps. Also, we present the spectrum adjunction in this approximation setting.

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