Bifibrational duality in non-abelian algebra and the theory of databases

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dc.contributor.advisorJanelidze, Zuraben_ZA
dc.contributor.authorWeighill, Thomasen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Department of Mathematical Sciences.en_ZA
dc.date.accessioned2015-01-13T11:50:38Z
dc.date.available2015-01-13T11:50:38Z
dc.date.issued2014-12en_ZA
dc.descriptionThesis (MSc)--Stellenbosch University, 2014.en_ZA
dc.description.abstractENGLISH ABSTRACT: In this thesis we develop a self-dual categorical approach to some topics in non-abelian algebra, which is based on replacing the framework of a category with that of a category equipped with a functor to it. We also make some first steps towards a possible link between this theory and the theory of databases in computer science. Both of these theories are based around the study of Grothendieck bifibrations and their generalisations. The main results in this thesis concern correspondences between certain structures on a category which are relevant to the study of categories of non-abelian group-like structures, and functors over that category. An investigation of these correspondences leads to a system of dual axioms on a functor, which can be considered as a solution to the proposal of Mac Lane in his 1950 paper "Duality for Groups" that a self-dual setting for formulating and proving results for groups be found. The part of the thesis concerned with the theory of databases is based on a recent approach by Johnson and Rosebrugh to views of databases and the view update problem.en
dc.description.abstractAFRIKAANSE OPSOMMING: In hierdie tesis word ’n self-duale kategoriese benadering tot verskeie onderwerpe in nie-abelse algebra ontwikkel, wat gebaseer is op die vervanging van die raamwerk van ’n kategorie met dié van ’n kategorie saam met ’n funktor tot die kategorie. Ons neem ook enkele eerste stappe in die rigting van ’n skakel tussen hierdie teorie and die teorie van databasisse in rekenaarwetenskap. Beide hierdie teorieë is gebaseer op die studie van Grothendieck bifibrasies en hul veralgemenings. Die hoof resultate in hierdie tesis het betrekking tot ooreenkomste tussen sekere strukture op ’n kategorie wat relevant tot die studie van nie-abelse groep-agtige strukture is, en funktore oor daardie kategorie. ’n Verdere ondersoek van hierdie ooreemkomste lei tot ’n sisteem van duale aksiomas op ’n funktor, wat beskou kan word as ’n oplossing tot die voorstel van Mac Lane in sy 1950 artikel “Duality for Groups” dat ’n self-duale konteks gevind word waarin resultate vir groepe geformuleer en bewys kan word. Die deel van hierdie tesis wat met die teorie van databasisse te doen het is gebaseer op ’n onlangse benadering deur Johnson en Rosebrugh tot aansigte van databasisse en die opdatering van hierdie aansigte.af_ZA
dc.format.extentviii, 115 p. : ill.
dc.identifier.urihttp://hdl.handle.net/10019.1/96125
dc.language.isoenen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subjectGrothendieck fibrationsen_ZA
dc.subjectDatabase theoryen_ZA
dc.subjectComputer science -- Mathematicsen_ZA
dc.subjectGroup theoryen_ZA
dc.subjectGrandis exact categoryen_ZA
dc.subjectNon-abelian algebraen_ZA
dc.subjectUCTDen_ZA
dc.subjectDissertations -- Mathematicsen_ZA
dc.subjectTheses -- Mathematicsen_ZA
dc.subjectGrothendieck groupsen_ZA
dc.subjectNon-Abelian groupsen_ZA
dc.titleBifibrational duality in non-abelian algebra and the theory of databasesen_ZA
dc.typeThesisen_ZA
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