Least change view-updating for functorial view-gets with left adjoints
thesisposted on 2022-03-28, 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.