Investigations into the categorical foundations of homotopy theory

 

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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


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