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Category Theory and Computer Science pp 290–300Cite as

A category of Galois connections

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Part of the book series: Lecture Notes in Computer Science ((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.

This research was partially funded by the National Science Foundation under grant DCR-8604080.

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Author information

Authors and Affiliations

  1. Department of Mathematics, California Polytechnic State University, 93407, San Luis Obispo, CA

    J. M. McDill

  2. Department of Computing and Information Sciences, Kansas State University, 66506, Manhattan, KS

    A. C. Melton

  3. Department of Mathematics, Kansas State University, 66506, Manhattan, KS

    G. E. Strecker

Authors
  1. J. M. McDill
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  2. A. C. Melton
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  3. G. E. Strecker
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Editor information

David H. Pitt Axel Poigné David E. Rydeheard

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© 1987 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/3-540-18508-9_32

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  • DOI: https://doi.org/10.1007/3-540-18508-9_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18508-6

  • Online ISBN: 978-3-540-48006-8

  • eBook Packages: Springer Book Archive

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