A correspondence between proximity homomorphisms and certain frame maps via a comonad
Category Theory
2024-07-17 v1
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 {\em stable compactification} (\cite{BezHar2}). We show that the frame of round ideals naturally carries with it two proximities of interest from which two comonads are induced.
Cite
@article{arxiv.2407.11528,
title = {A correspondence between proximity homomorphisms and certain frame maps via a comonad},
author = {Ando Razafindrakoto},
journal= {arXiv preprint arXiv:2407.11528},
year = {2024}
}