A category of Galois connections
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We study Galois connections by examining the properties of three categories. The objects in each category are Galois connections. The categories differ in their hom-sets; in the most general category the morphisms are pairs of functions which commute with the maps of the domain and codomain Galois connections. One of our main results is that one of the categories—the one which is the most closely related to the closed and open elements of the Galois connections—is Cartesian-closed.
- Blyth, T. S., and Janowitz, M. F. Residuation Theory. Pergammon Press, Oxford, 1972.
- Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M., and Scott, D.S. A Compendium of Continuous Lattices. Springer-Verlag, Berlin, 1980.
- Herrlich, H. and Husek, M. Galois connections. Springer-Verlag Lecture Notes in Computer Science, 239(1986), 122–134.
- Herrlich, H. and Strecker, G. E. Category Theory. Allyn and Bacon, Boston, 1973; second edition Helderman Verlag, Berlin, 1979.
- Melton, A., Schmidt, D. A., and Strecker, G. E. Galois connections and computer science applications. Springer-Verlag Lecture Notes in Computer Science, 240(1986), 299–312.
- Nielson, F. A denotational framework for data flow analysis. Acta Informatica, 18(1982), 265–287.
- Ore, O. Galois connections. Trans. Amer. Math. Soc. 55(1944), 493–513.
- Plotkin, G. The category of complete partial orders. Postgraduate course notes, Computer Science Dept., Edinburgh University, Edinburgh, Scotland, 1982.
- Schmidt, J. Beiträge zur Filtertheorie. II. Math. Nachr. 10(1953), 197–232.
- Scott, D. Continuous Lattices. Springer-Verlag Lecture Notes in Math. 274 (1972), 97–136.
- A category of Galois connections
- Book Title
- Category Theory and Computer Science
- Book Subtitle
- Edinburgh, U.K., September 7–9, 1987 Proceedings
- pp 290-300
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- Series Title
- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- Author Affiliations
- 1. Department of Mathematics, California Polytechnic State University, 93407, San Luis Obispo, CA
- 2. Department of Computing and Information Sciences, Kansas State University, 66506, Manhattan, KS
- 3. Department of Mathematics, Kansas State University, 66506, Manhattan, KS
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