{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/17169"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/17169","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Investigations into the categorical foundations of homotopy theory","abstract":"The purpose of the thesis is twofold - to give an account of the categorical foundations of homotopy theory, and to illuminate some aspects of category theory by showing the role played by the formation or quotient categories in many parts of general theory. Chapter 1 defines and classifies various types of quotient functor and gives methods of construction. Chapter 2 gives examples of the behaviour of limits under quotient functors. Chapter 3 defines the concepts of a weakly representable functor and a (general) homotopy theory and characterizes them. Chapter 4 develops some theory on the structure of abelian categories in order to produce a pathological example of a homotopy theory. Chapter 5 embeds the quotient categories constructed from homotopy theories in complete categories.","abstract_html":"The purpose of the thesis is twofold - to give an account of the categorical foundations of homotopy theory, and to illuminate some aspects of category theory by showing the role played by the formation or quotient categories in many parts of general theory. Chapter 1 defines and classifies various types of quotient functor and gives methods of construction. Chapter 2 gives examples of the behaviour of limits under quotient functors. Chapter 3 defines the concepts of a weakly representable functor and a (general) homotopy theory and characterizes them. Chapter 4 develops some theory on the structure of abelian categories in order to produce a pathological example of a homotopy theory. Chapter 5 embeds the quotient categories constructed from homotopy theories in complete categories.","abstract_has_math":false,"creators":["Hughes, Kenneth Robert"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Hardie, K A"],"committee_chairs":[],"committee_members":[],"year":1969,"date_issued":"1969","date_published":"1969","updated_at":"2026-07-22T22:22:52Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/17169","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hardie, K A"]},{"key":"dc:creator","label":"Author","values":["Hughes, Kenneth Robert"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-02-22T07:16:02Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-22T07:16:02Z"]},{"key":"dc:date.issued","label":"Date","values":["1969"]},{"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":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/17169"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The purpose of the thesis is twofold - to give an account of the categorical foundations of homotopy theory, and to illuminate some aspects of category theory by showing the role played by the formation or quotient categories in many parts of general theory. Chapter 1 defines and classifies various types of quotient functor and gives methods of construction. Chapter 2 gives examples of the behaviour of limits under quotient functors. Chapter 3 defines the concepts of a weakly representable functor and a (general) homotopy theory and characterizes them. Chapter 4 develops some theory on the structure of abelian categories in order to produce a pathological example of a homotopy theory. Chapter 5 embeds the quotient categories constructed from homotopy theories in complete categories."]},{"key":"dc:title","label":"Title","values":["Investigations into the categorical foundations of homotopy theory"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hardie, K A"],"dc:creator":["Hughes, Kenneth Robert"],"dc:date.accessioned":["2016-02-22T07:16:02Z"],"dc:date.available":["2016-02-22T07:16:02Z"],"dc:date.issued":["1969"],"dc:description.abstract":["The purpose of the thesis is twofold - to give an account of the categorical foundations of homotopy theory, and to illuminate some aspects of category theory by showing the role played by the formation or quotient categories in many parts of general theory. Chapter 1 defines and classifies various types of quotient functor and gives methods of construction. Chapter 2 gives examples of the behaviour of limits under quotient functors. Chapter 3 defines the concepts of a weakly representable functor and a (general) homotopy theory and characterizes them. Chapter 4 develops some theory on the structure of abelian categories in order to produce a pathological example of a homotopy theory. Chapter 5 embeds the quotient categories constructed from homotopy theories in complete categories."],"dc:identifier.uri":["http://hdl.handle.net/11427/17169"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Investigations into the categorical foundations of homotopy theory"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-22T22:22:52Z"}