On the value of commutative diagrams in information modelling
Category theory has been widely used in computer science, but usually in a very sophisticated manner. This paper argues that elementary category theoretic notions can have important value in the “real world” of software engineering. Perhaps the most elementary categorical notion is that of commutative diagram. Drawing on experience from several applications of category theory to information modelling in major business enterprises we show how commutative diagrams have been used to develop new methodologies in ER-modelling, constraint specification and process modelling. They also suggest new but as yet untested techniques for information model partitioning and information system architecture. The methodologies described here have a firm theoretical basis using the recently isolated theory of lextensive categories and this basis is briefly outlined.
KeywordsCommutative Diagram Static Constraint Information Model Query Language Category Theory
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- M. Barr and C. Wells, Category theory and computer science.Prentice Hall, 1990.Google Scholar
- A. Carboni, S. Lack and R.F.C. Walters, Introduction to extensive and distributive categories, Pure Mathematics Report92–9, University of Sydney, 1992.Google Scholar
- C.N.G. Dampney, M. Johnson and P. Deuble, Taming large complex information systems in D.G. Green and T. Bossomaier (eds) Complex Systems IOS Press, Amsterdam, (1993), 210–222.Google Scholar
- C.N.G. Dampney, M. Johnson and G.P. Monro, An illustrated mathematical foundation for ERA, in C.M.I. Rattray and R.G. Clarke (eds) The unified computation laboratory, Oxford University Press, Oxford, (1992), 77–84.Google Scholar
- CA. Gunther, The mixed power domain, to appear in Theoretical Computer Science.Google Scholar
- Saunders Mac Lane, Categories for the Working Mathematician, Graduate Texts in Mathematics 5, Springer-Verlag, 1971.Google Scholar
- R.F.C. Walters, Categories and computer science, Cambridge University Press, 1992.Google Scholar