{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/38111"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/38111","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Internal factorisation systems","abstract":"We introduce internal factorisation systems for internal categories. We recall the definitions and theory of internal categories and factorisation systems. We develop a diagrammatic calculus of pullbacks for ease of internal calculation. To define an internal factorisation system we define and study the subobjects of isomorphisms, an internalisation of the class of isomorphisms of a category. We provide an abstract example of an internal factorisation system. We then internalise various properties of factorisation systems, such as the two components determining each other, the cancellation properties and the essential uniqueness of factorisations, and show that an internal factorisation system satisfies these internal conditions.","abstract_html":"We introduce internal factorisation systems for internal categories. We recall the definitions and theory of internal categories and factorisation systems. We develop a diagrammatic calculus of pullbacks for ease of internal calculation. To define an internal factorisation system we define and study the subobjects of isomorphisms, an internalisation of the class of isomorphisms of a category. We provide an abstract example of an internal factorisation system. We then internalise various properties of factorisation systems, such as the two components determining each other, the cancellation properties and the essential uniqueness of factorisations, and show that an internal factorisation system satisfies these internal conditions.","abstract_has_math":false,"creators":["Ranchod, Sanjiv"],"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 Tamar"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023","date_published":"2023","updated_at":"2026-07-22T22:22:58Z","subjects":["Mathematics and Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/38111","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 Tamar"]},{"key":"dc:creator","label":"Author","values":["Ranchod, Sanjiv"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-07-14T11:18:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-07-14T11:18:38Z"]},{"key":"dc:date.issued","label":"Date","values":["2023"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters","MSc"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics and Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/38111"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We introduce internal factorisation systems for internal categories. We recall the definitions and theory of internal categories and factorisation systems. We develop a diagrammatic calculus of pullbacks for ease of internal calculation. To define an internal factorisation system we define and study the subobjects of isomorphisms, an internalisation of the class of isomorphisms of a category. We provide an abstract example of an internal factorisation system. We then internalise various properties of factorisation systems, such as the two components determining each other, the cancellation properties and the essential uniqueness of factorisations, and show that an internal factorisation system satisfies these internal conditions."]},{"key":"dc:title","label":"Title","values":["Internal factorisation systems"]}]}],"canonical_facts":{"dc:contributor.advisor":["Janelidze, George","Janelidze Tamar"],"dc:creator":["Ranchod, Sanjiv"],"dc:date.accessioned":["2023-07-14T11:18:38Z"],"dc:date.available":["2023-07-14T11:18:38Z"],"dc:date.issued":["2023"],"dc:description.abstract":["We introduce internal factorisation systems for internal categories. We recall the definitions and theory of internal categories and factorisation systems. We develop a diagrammatic calculus of pullbacks for ease of internal calculation. To define an internal factorisation system we define and study the subobjects of isomorphisms, an internalisation of the class of isomorphisms of a category. We provide an abstract example of an internal factorisation system. We then internalise various properties of factorisation systems, such as the two components determining each other, the cancellation properties and the essential uniqueness of factorisations, and show that an internal factorisation system satisfies these internal conditions."],"dc:identifier.uri":["http://hdl.handle.net/11427/38111"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["Mathematics and Applied Mathematics"],"dc:title":["Internal factorisation systems"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters","MSc"]},"updated_at":"2026-07-22T22:22:58Z"}