Coverings and Descent Theory of Finite Spaces

dc.contributor.advisorJanelidze, George
dc.contributor.authorMbewu, Thomas
dc.date.accessioned2023-03-30T12:59:25Z
dc.date.available2023-03-30T12:59:25Z
dc.date.issued2022
dc.date.updated2023-03-30T07:12:33Z
dc.description.abstractThis thesis presents the categorical Galois theory of the reflection of the category of finite topological spaces into the category of discrete finite topological spaces. This turns out to be nothing but the equivalence between the category of coverings of a connected finite topological space and the actions of the fundamental group of that space. Since some descent theory is necessary for categorical Galois theory, this thesis also contains an account of some of the descent theory of finite topological spaces. The reader is assumed to know the basics of category theory, but no descent theory or categorical Galois theory, or even internal category theory, but to be somewhat familiar with coverings and fundamental groups, and the notion of “locally” for topological spaces.
dc.identifier.apacitationMbewu, T. (2022). <i>Coverings and Descent Theory of Finite Spaces</i>. (). ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/37572en_ZA
dc.identifier.chicagocitationMbewu, Thomas. <i>"Coverings and Descent Theory of Finite Spaces."</i> ., ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2022. http://hdl.handle.net/11427/37572en_ZA
dc.identifier.citationMbewu, T. 2022. Coverings and Descent Theory of Finite Spaces. . ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/37572en_ZA
dc.identifier.ris TY - Master Thesis AU - Mbewu, Thomas AB - This thesis presents the categorical Galois theory of the reflection of the category of finite topological spaces into the category of discrete finite topological spaces. This turns out to be nothing but the equivalence between the category of coverings of a connected finite topological space and the actions of the fundamental group of that space. Since some descent theory is necessary for categorical Galois theory, this thesis also contains an account of some of the descent theory of finite topological spaces. The reader is assumed to know the basics of category theory, but no descent theory or categorical Galois theory, or even internal category theory, but to be somewhat familiar with coverings and fundamental groups, and the notion of “locally” for topological spaces. DA - 2022_ DB - OpenUCT DP - University of Cape Town KW - Mathematics and Applied Mathematics LK - https://open.uct.ac.za PY - 2022 T1 - Coverings and Descent Theory of Finite Spaces TI - Coverings and Descent Theory of Finite Spaces UR - http://hdl.handle.net/11427/37572 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/37572
dc.identifier.vancouvercitationMbewu T. Coverings and Descent Theory of Finite Spaces. []. ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2022 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/37572en_ZA
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.subjectMathematics and Applied Mathematics
dc.titleCoverings and Descent Theory of Finite Spaces
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMSc
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