Towards free localic algebras
The purpose of this paper is to establish that the underlying objectfunctor from the models of a Lawvere theory to the base category creates limitsand coequalisers of all parallel pairs of homomorphisms whose underlying pairadmit a split coequaliser. We show that for a small complete category witha...
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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_104757_bee44fcaa9faf23c1ff68f1d061466dd.pdf |
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| author | Nathan Tshakatumba Partha Pratim Ghosh Inderasan Naidoo |
| author_facet | Nathan Tshakatumba Partha Pratim Ghosh Inderasan Naidoo |
| author_sort | Nathan Tshakatumba |
| collection | DOAJ |
| description | The purpose of this paper is to establish that the underlying objectfunctor from the models of a Lawvere theory to the base category creates limitsand coequalisers of all parallel pairs of homomorphisms whose underlying pairadmit a split coequaliser. We show that for a small complete category witha well behaved proper factorisation structure, the underlying functor admitsa left adjoint and the category of such models is precisely monadic over thebase category in the sense of Beck’s Theorem. In particular, this establishesthe existence of free localic algebras for any Lawvere theory, generalising theknown results for the existence of free localic groups. |
| format | Article |
| id | doaj-art-88612d19888a4a6ea7c3ab651e322a9d |
| 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-88612d19888a4a6ea7c3ab651e322a9d2025-01-24T18:43:40ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612025-01-0122111313710.48308/cgasa.2024.233933.1445104757Towards free localic algebrasNathan Tshakatumba0Partha Pratim Ghosh1Inderasan Naidoo2Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003 Unisa, South Africa. National Institute for Theoretical and Computational Sciences (NITheCS), South Africa.Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003 Unisa, South Africa. National Institute for Theoretical and Computational Sciences (NITheCS), South Africa.Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003 Unisa, South Africa. National Institute for Theoretical and Computational Sciences (NITheCS), South Africa.The purpose of this paper is to establish that the underlying objectfunctor from the models of a Lawvere theory to the base category creates limitsand coequalisers of all parallel pairs of homomorphisms whose underlying pairadmit a split coequaliser. We show that for a small complete category witha well behaved proper factorisation structure, the underlying functor admitsa left adjoint and the category of such models is precisely monadic over thebase category in the sense of Beck’s Theorem. In particular, this establishesthe existence of free localic algebras for any Lawvere theory, generalising theknown results for the existence of free localic groups.https://cgasa.sbu.ac.ir/article_104757_bee44fcaa9faf23c1ff68f1d061466dd.pdfbeck's theoremfreyd's adjoint functor theoremco-well-powered categorylawvere theorymonadicitynearly ptt |
| spellingShingle | Nathan Tshakatumba Partha Pratim Ghosh Inderasan Naidoo Towards free localic algebras Categories and General Algebraic Structures with Applications beck's theorem freyd's adjoint functor theorem co-well-powered category lawvere theory monadicity nearly ptt |
| title | Towards free localic algebras |
| title_full | Towards free localic algebras |
| title_fullStr | Towards free localic algebras |
| title_full_unstemmed | Towards free localic algebras |
| title_short | Towards free localic algebras |
| title_sort | towards free localic algebras |
| topic | beck's theorem freyd's adjoint functor theorem co-well-powered category lawvere theory monadicity nearly ptt |
| url | https://cgasa.sbu.ac.ir/article_104757_bee44fcaa9faf23c1ff68f1d061466dd.pdf |
| work_keys_str_mv | AT nathantshakatumba towardsfreelocalicalgebras AT parthapratimghosh towardsfreelocalicalgebras AT inderasannaidoo towardsfreelocalicalgebras |