Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 22 1 2025 01 01 A correspondence between proximity homomorphisms and certain frame maps via a comonad 93 112 104668 10.48308/cgasa.2024.235267.1480 EN Ando Razafindrakoto Department of Mathematics and Applied Mathematics, Uiversity of the Western Cape, Bellville 7535, Cape Town, South Africa. Journal Article 2024 04 03 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 <em>stable</em> <em>compactification</em> ([6]). We show that the frame of round ideals naturally carries with it two proximities of interest from which two comonads are induced.  https://cgasa.sbu.ac.ir/article_104668_aac7c654e940fc838d81de463c34a144.pdf