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Characterization of coextensive varieties of universal algebras
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...
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| Format: | Thesis |
| Language: | English English |
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Department of Mathematics and Applied Mathematics
2025
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| _version_ | 1867613277776773120 |
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| access_status_str | Open Access |
| author | Broodryk, David Neal |
| author2 | Janelidze, George |
| author_browse | Broodryk, David Neal Janelidze, George |
| author_facet | Janelidze, George Broodryk, David Neal |
| author_sort | Broodryk, David Neal |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/42120 |
| institution | University of Cape Town (South Africa) |
| language | English eng |
| last_indexed | 2026-06-10T12:33:35.758Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/42120 Characterization of coextensive varieties of universal algebras Broodryk, David Neal Janelidze, George Janelidze-Gray, Tamar Algebras Mathematics 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. 2025-11-06T09:28:03Z 2025-11-06T09:28:03Z 2025 2025-11-06T09:26:46Z Thesis / Dissertation Doctoral PhD http://hdl.handle.net/11427/42120 en eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Algebras Mathematics Broodryk, David Neal Characterization of coextensive varieties of universal algebras |
| thesis_degree_str | Doctoral |
| title | Characterization of coextensive varieties of universal algebras |
| title_full | Characterization of coextensive varieties of universal algebras |
| title_fullStr | Characterization of coextensive varieties of universal algebras |
| title_full_unstemmed | Characterization of coextensive varieties of universal algebras |
| title_short | Characterization of coextensive varieties of universal algebras |
| title_sort | characterization of coextensive varieties of universal algebras |
| topic | Algebras Mathematics |
| url | http://hdl.handle.net/11427/42120 |
| work_keys_str_mv | AT broodrykdavidneal characterizationofcoextensivevarietiesofuniversalalgebras |