{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/42120"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/42120","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Characterization of coextensive varieties of universal algebras","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Broodryk, David Neal"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Janelidze, George","Janelidze-Gray, Tamar"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025","date_published":"2025","updated_at":"2026-07-22T22:23:14Z","subjects":["Algebras","Mathematics"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/42120","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Janelidze, George","Janelidze-Gray, Tamar"]},{"key":"dc:creator","label":"Author","values":["Broodryk, David Neal"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-11-06T09:28:03Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-11-06T09:28:03Z"]},{"key":"dc:date.issued","label":"Date","values":["2025"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Thesis / Dissertation"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral","PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebras","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/42120"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Characterization of coextensive varieties of universal algebras"]}]}],"canonical_facts":{"dc:contributor.advisor":["Janelidze, George","Janelidze-Gray, Tamar"],"dc:creator":["Broodryk, David Neal"],"dc:date.accessioned":["2025-11-06T09:28:03Z"],"dc:date.available":["2025-11-06T09:28:03Z"],"dc:date.issued":["2025"],"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.uri":["http://hdl.handle.net/11427/42120"],"dc:language.iso":["en"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:subject":["Algebras","Mathematics"],"dc:title":["Characterization of coextensive varieties of universal algebras"],"dc:type":["Thesis / Dissertation"],"dc:type.qualificationlevel":["Doctoral","PhD"]},"updated_at":"2026-07-22T22:23:14Z"}