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 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.

Grantor

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2022

Author dc:creator

• Brey, Khadija

Advisor dc:contributor.advisor

• Janelidze, George

• Mathematics and Applied Mathematics

Handle dc:identifier.uri

http://hdl.handle.net/11427/37095

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/37095