Geodesic
Approximate maps, filter monad, and a representation of localic maps
Archivum mathematicum, Tome 46 (2010) no. 4, pp. 285-298

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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.
Classification : 06D22, 18C20
Keywords: frames (locales); localic maps; approximation; Kleisli representation 
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     author = {Banaschewski, Bernhard and Pultr, Ale\v{s}},
     title = {Approximate maps, filter monad, and a representation of localic maps},
     journal = {Archivum mathematicum},
     pages = {285--298},
     publisher = {mathdoc},
     volume = {46},
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     zbl = {1240.06038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010__46_4_a4/}
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Banaschewski, Bernhard; Pultr, Aleš. Approximate maps, filter monad, and a representation of localic maps. Archivum mathematicum, Tome 46 (2010) no. 4, pp. 285-298. http://geodesic.mathdoc.fr/item/ARM_2010__46_4_a4/