Topics in categorical algebra and Galois theory

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dc.contributor.advisorJanelidze, Georgeen_ZA
dc.contributor.authorFourie, Jasonen_ZA
dc.date.accessioned2018-01-29T07:24:28Z
dc.date.available2018-01-29T07:24:28Z
dc.date.issued2017en_ZA
dc.description.abstractWe 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.en_ZA
dc.identifier.apacitationFourie, J. (2017). <i>Topics in categorical algebra and Galois theory</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/27061en_ZA
dc.identifier.chicagocitationFourie, Jason. <i>"Topics in categorical algebra and Galois theory."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017. http://hdl.handle.net/11427/27061en_ZA
dc.identifier.citationFourie, J. 2017. Topics in categorical algebra and Galois theory. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Fourie, Jason AB - 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. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - Topics in categorical algebra and Galois theory TI - Topics in categorical algebra and Galois theory UR - http://hdl.handle.net/11427/27061 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/27061
dc.identifier.vancouvercitationFourie J. Topics in categorical algebra and Galois theory. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/27061en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleTopics in categorical algebra and Galois theoryen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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