Formal Models of Object-Oriented Databases

Abstract. 3 This article summarizes mathematical formalisms used to describe ob-ject and object-oriented databases. Different approaches were used to describe object databases, object database models respectively. We fo-cus on algebraic approaches including graphs, monoid comprehensions, monads and semi-monads, and applied type theory. Especially we intro-duce formal categorical approach to object database modeling. Several categorical models of object databases are described as well as model