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Investigations into the categorical foundations of homotopy theory
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...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613210895450112 |
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| access_status_str | Open Access |
| author | Hughes, Kenneth Robert |
| author2 | Hardie, K A |
| author_browse | Hardie, K A Hughes, Kenneth Robert |
| author_facet | Hardie, K A Hughes, Kenneth Robert |
| author_sort | Hughes, Kenneth Robert |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17169 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:31.718Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/17169 Investigations into the categorical foundations of homotopy theory Hughes, Kenneth Robert Hardie, K A Mathematics 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. 2016-02-22T07:16:02Z 2016-02-22T07:16:02Z 1969 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/17169 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Hughes, Kenneth Robert Investigations into the categorical foundations of homotopy theory |
| thesis_degree_str | Doctoral |
| title | Investigations into the categorical foundations of homotopy theory |
| title_full | Investigations into the categorical foundations of homotopy theory |
| title_fullStr | Investigations into the categorical foundations of homotopy theory |
| title_full_unstemmed | Investigations into the categorical foundations of homotopy theory |
| title_short | Investigations into the categorical foundations of homotopy theory |
| title_sort | investigations into the categorical foundations of homotopy theory |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/17169 |
| work_keys_str_mv | AT hugheskennethrobert investigationsintothecategoricalfoundationsofhomotopytheory |