Characterization of coextensive varieties of universal algebras
| dc.contributor.advisor | Janelidze, George | |
| dc.contributor.advisor | Janelidze-Gray, Tamar | |
| dc.contributor.author | Broodryk, David Neal | |
| dc.date.accessioned | 2025-11-06T09:28:03Z | |
| dc.date.available | 2025-11-06T09:28:03Z | |
| dc.date.issued | 2025 | |
| dc.date.updated | 2025-11-06T09:26:46Z | |
| dc.description.abstract | A coextensive category can be defined as a category C with finite products such that for each pair X, Y of objects in C, the canonical functor × : X/C × Y /C / / (X × Y )/C is an equivalence. In this thesis we give a syntactic characterization of coextensive varieties of universal algebras. We first show that any such variety must have what we call a diagonalizing term. The existence of such a term is a Mal'tsev condition which is interesting in its own right, and we show that it is sufficient to prove many useful subconditions of coextensivity. We also introduce the notion of a category with upward closed subproducts as a categorical generalization of varieties with diagonalizing terms, which we study in the more general context of Barr-exact categories. | |
| dc.identifier.apacitation | Broodryk, D. N. (2025). <i>Characterization of coextensive varieties of universal algebras</i>. (). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/42120 | en_ZA |
| dc.identifier.chicagocitation | Broodryk, David Neal. <i>"Characterization of coextensive varieties of universal algebras."</i> ., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2025. http://hdl.handle.net/11427/42120 | en_ZA |
| dc.identifier.citation | Broodryk, D.N. 2025. Characterization of coextensive varieties of universal algebras. . University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/42120 | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Broodryk, David Neal AB - A coextensive category can be defined as a category C with finite products such that for each pair X, Y of objects in C, the canonical functor × : X/C × Y /C / / (X × Y )/C is an equivalence. In this thesis we give a syntactic characterization of coextensive varieties of universal algebras. We first show that any such variety must have what we call a diagonalizing term. The existence of such a term is a Mal'tsev condition which is interesting in its own right, and we show that it is sufficient to prove many useful subconditions of coextensivity. We also introduce the notion of a category with upward closed subproducts as a categorical generalization of varieties with diagonalizing terms, which we study in the more general context of Barr-exact categories. DA - 2025 DB - OpenUCT DP - University of Cape Town KW - Algebras KW - Mathematics LK - https://open.uct.ac.za PB - University of Cape Town PY - 2025 T1 - Characterization of coextensive varieties of universal algebras TI - Characterization of coextensive varieties of universal algebras UR - http://hdl.handle.net/11427/42120 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/42120 | |
| dc.identifier.vancouvercitation | Broodryk DN. Characterization of coextensive varieties of universal algebras. []. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2025 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/42120 | en_ZA |
| dc.language.iso | en | |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Department of Mathematics and Applied Mathematics | |
| dc.publisher.faculty | Faculty of Science | |
| dc.publisher.institution | University of Cape Town | |
| dc.subject | Algebras | |
| dc.subject | Mathematics | |
| dc.title | Characterization of coextensive varieties of universal algebras | |
| dc.type | Thesis / Dissertation | |
| dc.type.qualificationlevel | Doctoral | |
| dc.type.qualificationlevel | PhD |