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dc.contributor.advisor | Hardie, K A | en_ZA |

dc.contributor.author | Hughes, Kenneth Robert | en_ZA |

dc.date.accessioned | 2016-02-22T07:16:02Z | |

dc.date.available | 2016-02-22T07:16:02Z | |

dc.date.issued | 1969 | en_ZA |

dc.identifier.citation | Hughes, K. 1969. Investigations into the categorical foundations of homotopy theory. University of Cape Town. | en_ZA |

dc.identifier.uri | http://hdl.handle.net/11427/17169 | |

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. | en_ZA |

dc.language.iso | eng | en_ZA |

dc.subject.other | Mathematics | en_ZA |

dc.title | Investigations into the categorical foundations of homotopy theory | en_ZA |

dc.type | Doctoral Thesis | |

uct.type.publication | Research | en_ZA |

uct.type.resource | Thesis | en_ZA |

dc.publisher.institution | University of Cape Town | |

dc.publisher.faculty | Faculty of Science | en_ZA |

dc.publisher.department | Department of Mathematics and Applied Mathematics | en_ZA |

dc.type.qualificationlevel | Doctoral | |

dc.type.qualificationname | PhD | en_ZA |

uct.type.filetype | Text | |

uct.type.filetype | Image | |

dc.identifier.apacitation | Hughes, K. R. (1969). <i>Investigations into the categorical foundations of homotopy theory</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17169 | en_ZA |

dc.identifier.chicagocitation | Hughes, Kenneth Robert. <i>"Investigations into the categorical foundations of homotopy theory."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1969. http://hdl.handle.net/11427/17169 | en_ZA |

dc.identifier.vancouvercitation | Hughes KR. Investigations into the categorical foundations of homotopy theory. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1969 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17169 | en_ZA |

dc.identifier.ris | TY - Thesis / Dissertation AU - Hughes, Kenneth Robert AB - 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. DA - 1969 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1969 T1 - Investigations into the categorical foundations of homotopy theory TI - Investigations into the categorical foundations of homotopy theory UR - http://hdl.handle.net/11427/17169 ER - | en_ZA |