A category of Galois connections

  • J. M. McDill
  • A. C. Melton
  • G. E. Strecker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 283)

Abstract

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.

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7. References

  1. [BJ]
    Blyth, T. S., and Janowitz, M. F. Residuation Theory. Pergammon Press, Oxford, 1972.Google Scholar
  2. [G]
    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.Google Scholar
  3. [HH]
    Herrlich, H. and Husek, M. Galois connections. Springer-Verlag Lecture Notes in Computer Science, 239(1986), 122–134.Google Scholar
  4. [HS]
    Herrlich, H. and Strecker, G. E. Category Theory. Allyn and Bacon, Boston, 1973; second edition Helderman Verlag, Berlin, 1979.Google Scholar
  5. [MSS]
    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.Google Scholar
  6. [N]
    Nielson, F. A denotational framework for data flow analysis. Acta Informatica, 18(1982), 265–287.Google Scholar
  7. [O]
    Ore, O. Galois connections. Trans. Amer. Math. Soc. 55(1944), 493–513.Google Scholar
  8. [P]
    Plotkin, G. The category of complete partial orders. Postgraduate course notes, Computer Science Dept., Edinburgh University, Edinburgh, Scotland, 1982.Google Scholar
  9. [Sch]
    Schmidt, J. Beiträge zur Filtertheorie. II. Math. Nachr. 10(1953), 197–232.Google Scholar
  10. [S]
    Scott, D. Continuous Lattices. Springer-Verlag Lecture Notes in Math. 274 (1972), 97–136.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. M. McDill
    • 1
  • A. C. Melton
    • 2
  • G. E. Strecker
    • 3
  1. 1.Department of MathematicsCalifornia Polytechnic State UniversitySan Luis Obispo
  2. 2.Department of Computing and Information SciencesKansas State UniversityManhattan
  3. 3.Department of MathematicsKansas State UniversityManhattan

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