A correspondence between proximity homomorphisms and certain frame maps via a comonad
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 natural...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2025-01-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | https://cgasa.sbu.ac.ir/article_104668_aac7c654e940fc838d81de463c34a144.pdf |
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| _version_ | 1832586952745943040 |
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| author | Ando Razafindrakoto |
| author_facet | Ando Razafindrakoto |
| author_sort | Ando Razafindrakoto |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b1074480c8624b5fb83411af4c2f55fb |
| institution | Kabale University |
| issn | 2345-5853 2345-5861 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj-art-b1074480c8624b5fb83411af4c2f55fb2025-01-24T18:43:40ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612025-01-012219311210.48308/cgasa.2024.235267.1480104668A correspondence between proximity homomorphisms and certain frame maps via a comonadAndo Razafindrakoto0Department of Mathematics and Applied Mathematics, Uiversity of the Western Cape, Bellville 7535, Cape Town, South Africa.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.https://cgasa.sbu.ac.ir/article_104668_aac7c654e940fc838d81de463c34a144.pdfproximity homomorphismround idealstably compact framecompactificationmonadalgebraskleisli composition |
| spellingShingle | Ando Razafindrakoto A correspondence between proximity homomorphisms and certain frame maps via a comonad Categories and General Algebraic Structures with Applications proximity homomorphism round ideal stably compact frame compactification monad algebras kleisli composition |
| title | A correspondence between proximity homomorphisms and certain frame maps via a comonad |
| title_full | A correspondence between proximity homomorphisms and certain frame maps via a comonad |
| title_fullStr | A correspondence between proximity homomorphisms and certain frame maps via a comonad |
| title_full_unstemmed | A correspondence between proximity homomorphisms and certain frame maps via a comonad |
| title_short | A correspondence between proximity homomorphisms and certain frame maps via a comonad |
| title_sort | correspondence between proximity homomorphisms and certain frame maps via a comonad |
| topic | proximity homomorphism round ideal stably compact frame compactification monad algebras kleisli composition |
| url | https://cgasa.sbu.ac.ir/article_104668_aac7c654e940fc838d81de463c34a144.pdf |
| work_keys_str_mv | AT andorazafindrakoto acorrespondencebetweenproximityhomomorphismsandcertainframemapsviaacomonad AT andorazafindrakoto correspondencebetweenproximityhomomorphismsandcertainframemapsviaacomonad |