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Fractoids
This dissertation will examine the properties of the algebraic structure herein named the fractoid. This structure will be defined and its properties closely examined. In this dissertation we will first provide context for this structure, by looking at both category theory and universal algebra. We...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2023
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| _version_ | 1867613317730664448 |
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| access_status_str | Open Access |
| author | Brey, Khadija |
| author2 | Janelidze, George |
| author_browse | Brey, Khadija Janelidze, George |
| author_facet | Janelidze, George Brey, Khadija |
| author_sort | Brey, Khadija |
| collection | Thesis |
| description | This dissertation will examine the properties of the algebraic structure herein named the fractoid. This structure will be defined and its properties closely examined. In this dissertation we will first provide context for this structure, by looking at both category theory and universal algebra. We present some first basic concepts of category theory and consider F-algebras (= algebras over an endofunctor F). We will then look at algebras in the sense of universal algebra. We will examine F-algebras and their properties in this context and compare them to the definitions used in some of the standard textbooks in universal algebra. Once fractoids are defined and examined, they will be compared to a similar existing algebraic structure, the wheel. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/37095 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:14.045Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| 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:11427/37095 Fractoids Brey, Khadija Janelidze, George Mathematics and Applied Mathematics This dissertation will examine the properties of the algebraic structure herein named the fractoid. This structure will be defined and its properties closely examined. In this dissertation we will first provide context for this structure, by looking at both category theory and universal algebra. We present some first basic concepts of category theory and consider F-algebras (= algebras over an endofunctor F). We will then look at algebras in the sense of universal algebra. We will examine F-algebras and their properties in this context and compare them to the definitions used in some of the standard textbooks in universal algebra. Once fractoids are defined and examined, they will be compared to a similar existing algebraic structure, the wheel. 2023-03-02T07:37:59Z 2023-03-02T07:37:59Z 2022 2023-02-20T12:19:54Z Master Thesis Masters MSc http://hdl.handle.net/11427/37095 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Brey, Khadija Fractoids |
| thesis_degree_str | Master's |
| title | Fractoids |
| title_full | Fractoids |
| title_fullStr | Fractoids |
| title_full_unstemmed | Fractoids |
| title_short | Fractoids |
| title_sort | fractoids |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/37095 |
| work_keys_str_mv | AT breykhadija fractoids |