Banaschewski, Bernhard; Pultr, Aleš Approximate maps, filter monad, and a representation of localic maps. (English) Zbl 1240.06038 Arch. Math., Brno 46, No. 4, 285-298 (2010). 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. Cited in 1 Document MSC: 06D22 Frames, locales 18C20 Eilenberg-Moore and Kleisli constructions for monads Keywords:frames; locales; localic maps; approximation; Kleisli representation PDFBibTeX XMLCite \textit{B. Banaschewski} and \textit{A. Pultr}, Arch. Math., Brno 46, No. 4, 285--298 (2010; Zbl 1240.06038) Full Text: EuDML EMIS