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

[摘要] ENGLISH ABSTRACT: In this thesis we develop a self-dual categorical approach to some topics innon-abelian algebra, which is based on replacing the framework of a categorywith that of a category equipped with a functor to it. We also make some firststeps towards a possible link between this theory and the theory of databasesin computer science. Both of these theories are based around the study ofGrothendieck bifibrations and their generalisations. The main results in thisthesis concern correspondences between certain structures on a category whichare relevant to the study of categories of non-abelian group-like structures, andfunctors over that category. An investigation of these correspondences leadsto a system of dual axioms on a functor, which can be considered as a solutionto the proposal of Mac Lane in his 1950 paper Duality for Groups thata 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 arecent approach by Johnson and Rosebrugh to views of databases and the viewupdate problem.

[发布机构] Stellenbosch University