Affiliations: School of Engineering and Computer Science, Victoria University of Wellington, New Zealand. hui.ma@ecs.vuw.ac.nz | Institute of Computer Science, Christian-Albrechts-University Kiel, Germany. noack@is.informatik.uni-kiel.de | Software Competence Center Hagenberg, Hagenberg, Austria. klaus-dieter.schewe@scch.at | Institute of Computer Science, Christian-Albrechts-University Kiel, Germany. thalheim@is.informatik.uni-kiel.de | Research School of Computer Science, The Australian National University, Canberra, Australia. qing.wang@anu.edu.au
Note: [] Address for correspondence: School of Engineering and Computer Science, Victoria University of Wellington, New Zealand
Abstract: A schema algebra comprises operations on database schemata for a given data model. Such algebras are useful in database design as well as in schema integration. In this article we address the necessary theoretical underpinnings by introducing a novel notion of conceptual schema morphism that captures at the same time the conceptual schema and its semantics by means of the set of valid instances. This leads to a category of schemata that is finitely complete and co-complete. This is the basis for a notion of completeness of schema algebras, if it captures all universal constructions in the category of schemata. We exemplify this notion of completeness for a recently introduced particular schema algebra.
