A correspondence between proximity homomorphisms and certain frame maps via a comonad

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Document Type : Research Paper

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Department of Mathematics and Applied Mathematics, Uiversity of the Western Cape, Bellville 7535, Cape Town, South Africa.

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 ([6]). 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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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 15 July 2024

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