A correspondence between proximity homomorphisms and certain frame maps via a comonad
Abstract
We exhibit the proximity frames and proximity homomorphisms as a Kleisli category of a comonad whose underlying functor takes a proximity frame to its frame of round ideals. This construction is known in the literature as stable compactification (BezHar2). We show that the frame of round ideals naturally carries with it two proximities of interest from which two comonads are induced.
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