Saturation of the morphisms in the database category

TL;DR

This paper investigates the saturation phenomenon of morphisms in the database category DB, providing an algorithm to compute saturated morphisms that enhance the expressiveness of schema mappings in data integration.

Contribution

It introduces the concept of saturation for morphisms in DB and presents an algorithm to compute saturated morphisms, improving the understanding of schema mappings in data integration.

Findings

Saturation can be algorithmically achieved for morphisms in DB.

Saturated morphisms are equivalent to original ones in any commutative diagram.

Saturation enhances the expressive power of schema mappings.

Abstract

In this paper we present the problem of saturation of a given morphism in the database category DB, which is the base category for the functiorial semantics of the database schema mapping systems used in Data Integration theory. This phenomena appears in the case when we are using the Second-Order tuple-generating dependencies (SOtgd) with existentially quantified non-built-in functions, for the database schema mappings. We provide the algorithm of the saturation for a given morphism, which represents a mapping between two relational databases, and show that the original morphism in DB can be equivalently substituted by its more powerful saturated version in any commutative diagram in DB.