Abstract
Egghe's continuous information production processes (in short IPP's) are described using category theory. Therefore, we first review the main ingredients of this mathematical theory, introduced byEilenberg andMac Lane more than four decades ago. Then we show how the notion of duality, as used byEgghe, can be placed in the abstract framework of categorical duality. This leads to a natural isomorphism involving the identity functor on a category of continuous IPP's. This natural isomorphism is completely similar to the well-known natural isomorphism between a finite-dimensional vector space and its double dual. We further show that to develop Egghe's theory on IPP's one needs no other intervals than the unit interval.
Similar content being viewed by others
References
L. Egghe, The Duality of Informetric Systems with Applications to the Empirical Laws. Ph. D. thesis, The City University London (UK), 1989.
L. Egghe, The Duality of informetric systems with applications to the empirical laws,Journal of Information Science, 16 (1990) 17–27.
L. Egghe, R. Rousseau,Introduction to Informetrics, Elsevier, Amsterdam, 1990.
R. Rousseau, Relations between continuous versions of bibliometric laws,Journal of the American Society for Information Science, 41 (1990) 197–203.
S. Mac Lane,Categories for the Working Mathematician, Springer-Verlag, New York-Heidelberg-Berlin, 1971.
H. Herrlich, G. E. Strecker,Category Theory, Allyn and Bacon, Boston, 1973.
D.H. Pitt (Ed.),Category Theory and Computer Science, Lecture Notes in Computer Science. Vol. 389, Springer-Verlag, Berlin-New York, 1989.
M. Barr, C. Wells, Category Theory for Computer Scientists, Prentice-Hall, Englewood Cliffs, NJ, 1989.
F.W. Lawvere, The category of categories as a foundation for mathematics. In:Proceedings of the La Jolla Conference in Categorical Algebra (S. Eilenberg, D.K. Harrison, S. MacLane, H. Röhrl (Eds), Springer-Verlag, Berlin-New York, 1966, p.1–21.
J.L. Bell, Category theory and the foundations of mathematics,British Journal for the Philosophy of Science, 32 (1981) 349–358.
S. Eilenberg, S. Mac Lane, Natural isomorphisms in group theory,Proceedings of the American Academy of Science, USA, 28 (1942) 537–543.
S. Eilenberg, S. Mac Lane, General theory of natural equivalences,Transactions of the American Mathematical Society, 58 (1945) 231–294.
P. Hilton, Categorieën en functoren,Niko, 9 (1971) 85–100.
H.P. Zeiger, Ho's algorithm, commutative diagrams, and the uniqueness of minimal linear systems,Information and Control, 11 (1967) 71–79.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rousseau, R. Category theory and informetrics: Information production processes. Scientometrics 25, 77–87 (1992). https://doi.org/10.1007/BF02016848
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02016848