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A Counter-Example to Coherence in Cartesian Closed Categories

Published online by Cambridge University Press:  20 November 2018

M. E. Szabo
M. E. Szabo*
Affiliation:
S.G.W. Department of MathematicsConcordia University, Montreal, Quebec
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It follows from [3] that all morphisms of free closed categories on finite discrete categories are components of natural or “generalized” natural transformations, and from [8] that all hom-sets of such categories are finite. The purpose of this paper is to show that neither statement remains true if the categories are also assumed to be cartesian.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 111 - 114
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Eilenberg, S. and Kelly, G. M., A Generalization of the Functorial Calculus, J. Algebra 3 (1966), 366-375.Google Scholar
2. Kelly, G. M., On MacLane's Conditions for Coherence of Natural Associativities, Commutativities, etc., J. Algebra 4 (1964), 397-402.Google Scholar
3. Kelly, G. M. and MacLane, S., Coherence in Closed Categories, J. Pure and Applied Algebra 1 (1971), 97-140.Google Scholar
4. Lambek, J., Deductive Systems and Categories I, Math. Systems Theory 2 (1968), 287-318.Google Scholar
5. Lambek, J., Deductive Systems and Categories II, Lecture Notes in Mathematics 86, Springer, Berlin, 1969, 76-122.Google Scholar
6. MacLane, S., Natural Associativity and Commutativity, Rice Univ. Stud. 49 (1963), 28-46.Google Scholar
7. MacLane, S., Categories for the Working Mathematician, Springer, New York, 1971.Google Scholar
8. Szabo, M. E., The Logic of Closed Categories, Notre Dame Journal of Formal Logic, (to appear).Google Scholar