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Coverings and Descent Theory of Finite Spaces
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 th...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2023
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| _version_ | 1867613237629943808 |
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| access_status_str | Open Access |
| author | Mbewu, Thomas |
| author2 | Janelidze, George |
| author_browse | Janelidze, George Mbewu, Thomas |
| author_facet | Janelidze, George Mbewu, Thomas |
| author_sort | Mbewu, Thomas |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/37572 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:57.328Z |
| 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:11427/37572 Coverings and Descent Theory of Finite Spaces Mbewu, Thomas Janelidze, George Mathematics and Applied Mathematics 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. 2023-03-30T12:59:25Z 2023-03-30T12:59:25Z 2022 2023-03-30T07:12:33Z Master Thesis Masters MSc http://hdl.handle.net/11427/37572 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Mbewu, Thomas Coverings and Descent Theory of Finite Spaces |
| thesis_degree_str | Master's |
| title | Coverings and Descent Theory of Finite Spaces |
| title_full | Coverings and Descent Theory of Finite Spaces |
| title_fullStr | Coverings and Descent Theory of Finite Spaces |
| title_full_unstemmed | Coverings and Descent Theory of Finite Spaces |
| title_short | Coverings and Descent Theory of Finite Spaces |
| title_sort | coverings and descent theory of finite spaces |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/37572 |
| work_keys_str_mv | AT mbewuthomas coveringsanddescenttheoryoffinitespaces |