B.N. Rossiter
M.A. Heather
University of Newcastle upon Tyne. 1993
Database theory has had to be formalised at a single level in the past because appropriate mathematical formulations were not available as the technology was being developed. This report takes the point that a database is a functor and applies category theory as a multi-level formalism for database architecture. This approach allows us to formulate database concepts directly in mathematical terms. Previously database architecture had to be built up with extensions to set theory, now category theory is at the same level as database thinking. There emerges a natural and general mathematical architecture for databases with a functional data model. A clear advantage of this mathematical model is that it extends in an integrated and consistent fashion beyond the coverage of standard models demonstrating that the database concept operates from the highest conceptual level down to the technicalities of access and control of data storage area on the physical medium. Problem areas like functional dependencies can be clarified by exposing their functorial characteristics. However, the greatest asset of a functorial data model seems to be the ability to deal in a formal manner with global consistency.