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Least change view-updating for functorial view-gets with left adjoints

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posted on 28.03.2022, 21:16 authored by Ori Livson
Given a database, a view of it is a simplified version of that database, derived from some of its data, possibly through the output of query language expressions. This thesis is concerned with a category theoretic treatment of the View Update Problem, which is the problem of how to propagate a view update to an update of the original database. The basic Category Theoretic setting of interest to this thesis is that a database has an associated category S whose objects are valid states that the database can be in and some choice of valid updates as morphisms. A view of the database corresponding to S has its own state space V and a functor G : S - V, referred to as the view-get. So called least change view-update propagations have been studied in the categorical setting in papers stemming from, requiring that view-update propagations satisfy certain universal properties. This thesis studies the use of cartesian or opcartesian lifts as least change solutions to view-update problems. Moreover, the main contribution of this thesis are a pair of theorems pertaining to the existence of cartesian and opcartesian lifts respectively. The setting of these theorems involves G having a left adjoint L - G such that GL = idV.

History

Table of Contents

1. Introduction -- 2. Preliminary concepts in relational database theory -- 3. The sketch data model -- 4. View updating for view-gets with left adjoints -- 5. Special topics -- 6. Related work -- 7. Conclusion -- References.

Notes

Empirical thesis. Bibliography: pages 61-63

Awarding Institution

Macquarie University

Degree Type

Thesis MRes

Degree

MRes, Macquarie University, Faculty of Science an Engineering, Department of Mathematics

Department, Centre or School

Department of Mathematics

Year of Award

2018

Principal Supervisor

Michael Johnson

Rights

Copyright Ori Livson 2018. Copyright disclaimer: http://mq.edu.au/library/copyright

Language

English

Extent

1 online resource (iv, 63 pages) : diagrams

Former Identifiers

mq:70596 http://hdl.handle.net/1959.14/1265824