Categorical models of relational databases I: Fibrational formulation, schema integration

Abstract

This paper uses category theory to provide a formal mathematical framework for specifying and integrating relational database schemas; it builds on the work of Buneman et al. [2], who develop a domain-theoretic version of relational database theory. We generalize their setting in the following way: we let a schema be a functor V from a category L of attribute names to the category of domains; this reflects the fact that attributes may take values of different types, and that there may be functional constraints between attributes. As an application, we show how the process of schema integration and the resolution of conflicts between schemas may be carried out in a mathematically rigorous setting, using simple concepts from category theory; this proposal is shown to be consistent with the way in which queries on a federated database are processed (by 'distributing' them among its component databases).