A category of Galois connections

  • J. M. McDill
  • A. C. Melton
  • G. E. Strecker
Conference paper

DOI: 10.1007/3-540-18508-9_32

Volume 283 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
McDill J.M., Melton A.C., Strecker G.E. (1987) A category of Galois connections. In: Pitt D.H., Poigné A., Rydeheard D.E. (eds) Category Theory and Computer Science. Lecture Notes in Computer Science, vol 283. Springer, Berlin, Heidelberg

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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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