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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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| Summary: | 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. |
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