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Structure Species and Constructive Functors

Published online by Cambridge University Press:  20 November 2018

Andrew A. Blanchard
Andrew A. Blanchard*
Affiliation:
United States Naval Academy, Annapolis, Maryland
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This communication is in essence a note tying together the structure theory of Bourbaki and the categorical structure theory exemplified in the works of Sonner, and Hedrlin, Pultr, and Trnkova, to name a few. The work of Bourbaki [1] appeared in 1957, and quietly succumbed to the explosion of category theory. Sonner [6] used the nomenclature of Bourbaki to classify certain types of functors, while Hedrlin et al use the functor approach, studying structures by way of the associated forgetful functors. More discussion of this approach appears in section 3.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1217 - 1227
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bourbaki, N., Elements de mathématique: théorie des ensembles, Chapter 4 (Hermann, Paris, 1957).Google Scholar
2. Gabriel, P. and Zisman, M., Calculus of fractions and homotopy theory (Springer-Verlag, New York, 1967).Google Scholar
3. Hedrlin, Z., Pultr, A., and Trnkova, V., Concerning a categorical approach to topological and algebraic theories, General Topology and its Relations to Modern Analysis and Algebra, II, Proc. Second Prague Topological Symposium, 1966 (Academia, Prague, 1967).Google Scholar
4. MacLane, S., Categories for the working mathematician (Springer-Verlag, New York, 1971).Google Scholar
5. Pultr, A., On full embeddings of concrete categories with respect to forgetful functors, Comment. Math. Univ. Carolinae 9 (1968), 281–305.Google Scholar
6. Sonner, J., Lifting inductive and projective limits, Can. J. Math. 19 (1967), 1329–1339.Google Scholar