Relational data models and category theory (abstract)

Mathematicians use the notion of category to define their universe. While database theorists use the data model to define their universe of discourse. Therefore, a close interconnection between these two disciplines should be anticipated. This paper represents our first effort to explore this interconnection. Our present focus is on the categorical constructions of data modeling. Our approach encompasses many of current data models, relational models [Codd79], poset models [GiHu83], metric models [Motr86], Topological data models [Lin89], Power set models [BuPe82], and Sea View's Multilevel relational Data Models [Denn87]. This unification is economical both in concept and development. The categorical data models is not merely a conceptual unification of data modeling. In fact, this give us a framework of “generic database system”. And each individual system can then be obtained by specifying the category or the objects. We are developing a prototype of a generic DBMS for categorical data model. By specifying the category to that of graded sets the prototype DBMS will turn into a multilevel DBMS. There is a common misconception about the category theory; it is a very GENERAL mathematical theory. Category theory is a very HIGH level, but NOT very general, mathematical language. For example, category theory is not general enough to express any internal structure of its objects.