Investigations into the categorical foundations of homotopy theory

Simple item page
dc.contributor.advisorHardie, K Aen_ZA
dc.contributor.authorHughes, Kenneth Roberten_ZA
dc.date.accessioned2016-02-22T07:16:02Z
dc.date.available2016-02-22T07:16:02Z
dc.date.issued1969en_ZA
dc.description.abstractThe 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.identifier.apacitationHughes, 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/11427/17169en_ZA
dc.identifier.chicagocitationHughes, 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/11427/17169en_ZA
dc.identifier.citationHughes, K. 1969. Investigations into the categorical foundations of homotopy theory. University of Cape Town.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
dc.identifier.urihttp://hdl.handle.net/11427/17169
dc.identifier.vancouvercitationHughes 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/11427/17169en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleInvestigations into the categorical foundations of homotopy theoryen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
thesis_sci_1969_hughes_kenneth_robert.pdf
Size:
4.53 MB
Format:
Adobe Portable Document Format
Description:
Download
Collections
PhD / Doctoral