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Bifibrational duality in non-abelian algebra and the theory of databases
Thesis (MSc)--Stellenbosch University, 2014.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2015
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| _version_ | 1867614075872083968 |
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| access_status_str | Open Access |
| author | Weighill, Thomas |
| author2 | Janelidze, Zurab |
| author_browse | Janelidze, Zurab Weighill, Thomas |
| author_facet | Janelidze, Zurab Weighill, Thomas |
| author_sort | Weighill, Thomas |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2014. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/96125 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:46:16.958Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/96125 Bifibrational duality in non-abelian algebra and the theory of databases Weighill, Thomas Janelidze, Zurab Stellenbosch University. Faculty of Science. Department of Mathematical Sciences. Grothendieck fibrations Database theory Computer science -- Mathematics Group theory Grandis exact category Non-abelian algebra UCTD Dissertations -- Mathematics Theses -- Mathematics Grothendieck groups Non-Abelian groups Thesis (MSc)--Stellenbosch University, 2014. ENGLISH 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. AFRIKAANSE 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. 2015-01-13T11:50:38Z 2015-01-13T11:50:38Z 2014-12 Thesis http://hdl.handle.net/10019.1/96125 en Stellenbosch University viii, 115 p. : ill. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Grothendieck fibrations Database theory Computer science -- Mathematics Group theory Grandis exact category Non-abelian algebra UCTD Dissertations -- Mathematics Theses -- Mathematics Grothendieck groups Non-Abelian groups Weighill, Thomas Bifibrational duality in non-abelian algebra and the theory of databases |
| title | Bifibrational duality in non-abelian algebra and the theory of databases |
| title_full | Bifibrational duality in non-abelian algebra and the theory of databases |
| title_fullStr | Bifibrational duality in non-abelian algebra and the theory of databases |
| title_full_unstemmed | Bifibrational duality in non-abelian algebra and the theory of databases |
| title_short | Bifibrational duality in non-abelian algebra and the theory of databases |
| title_sort | bifibrational duality in non abelian algebra and the theory of databases |
| topic | Grothendieck fibrations Database theory Computer science -- Mathematics Group theory Grandis exact category Non-abelian algebra UCTD Dissertations -- Mathematics Theses -- Mathematics Grothendieck groups Non-Abelian groups |
| url | http://hdl.handle.net/10019.1/96125 |
| work_keys_str_mv | AT weighillthomas bifibrationaldualityinnonabelianalgebraandthetheoryofdatabases |