Abstract
It is well-known that Galois connections are useful in describing some situations that occur naturally in computer science and mathematics; and recently it has been shown that Lagois connections, which are closely related to Galois connections, are similarly useful. Thus, it is natural to ask if there are not common generalizations of Galois and Lagois connections which would be useful in both disciplines. In this paper we investigate several such generalizations. The primary one, called “connections”, was defined and first investigated in 1982 by H. Crapo. We present a hierarchy of connections from (general) connections to Lagois and Galois connections, and we establish properties of them. We also give examples in both computer science and mathematics.
The authors were partially funded by the the Office of Naval Research under Contract N00014-88-K-0455.
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© 1992 Springer-Verlag Berlin Heidelberg
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Melton, A., Schröder, B.S.W., Strecker, G.E. (1992). Connections. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1991. Lecture Notes in Computer Science, vol 598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55511-0_26
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DOI: https://doi.org/10.1007/3-540-55511-0_26
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