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Topics in categorical algebra and Galois theory
We provide an overview of the construction of categorical semidirect products and discuss their form in particular semi-abelian varieties. We then give a thorough description of categorical Galois theory, which yields an analogue for the fundamental theorem of Galois theory in an abstract category b...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2018
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| _version_ | 1867613256655306752 |
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| access_status_str | Open Access |
| author | Fourie, Jason |
| author2 | Janelidze, George |
| author_browse | Fourie, Jason Janelidze, George |
| author_facet | Janelidze, George Fourie, Jason |
| author_sort | Fourie, Jason |
| collection | Thesis |
| description | We provide an overview of the construction of categorical semidirect products and discuss their form in particular semi-abelian varieties. We then give a thorough description of categorical Galois theory, which yields an analogue for the fundamental theorem of Galois theory in an abstract category by making use of the notions of admissibility and effective descent. We show that the admissibility of a functor can be extended to the admissibility of the canonically induced functor on the associated category of pointed objects, and that an analogous extension can be made for effective descent morphisms. We use the extended notions of admissibility and effective descent to describe a new, pointed version of the categorical Galois theorem, and use this result to move the categorical formulation of the Galois theory of finite, separable field extensions into a non-unital context. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/27061 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:15.376Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| 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:11427/27061 Topics in categorical algebra and Galois theory Fourie, Jason Janelidze, George Mathematics We provide an overview of the construction of categorical semidirect products and discuss their form in particular semi-abelian varieties. We then give a thorough description of categorical Galois theory, which yields an analogue for the fundamental theorem of Galois theory in an abstract category by making use of the notions of admissibility and effective descent. We show that the admissibility of a functor can be extended to the admissibility of the canonically induced functor on the associated category of pointed objects, and that an analogous extension can be made for effective descent morphisms. We use the extended notions of admissibility and effective descent to describe a new, pointed version of the categorical Galois theorem, and use this result to move the categorical formulation of the Galois theory of finite, separable field extensions into a non-unital context. 2018-01-29T07:24:28Z 2018-01-29T07:24:28Z 2017 Master Thesis Masters MSc http://hdl.handle.net/11427/27061 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Fourie, Jason Topics in categorical algebra and Galois theory |
| thesis_degree_str | Master's |
| title | Topics in categorical algebra and Galois theory |
| title_full | Topics in categorical algebra and Galois theory |
| title_fullStr | Topics in categorical algebra and Galois theory |
| title_full_unstemmed | Topics in categorical algebra and Galois theory |
| title_short | Topics in categorical algebra and Galois theory |
| title_sort | topics in categorical algebra and galois theory |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/27061 |
| work_keys_str_mv | AT fouriejason topicsincategoricalalgebraandgaloistheory |