Galois connection

English

Alternative forms

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Etymology

From Template:M (attributive form of Template:M) + Template:M; ultimately after French mathematician Template:W. Coined by Norwegian mathematician Template:W in 1944, Galois connexions, Template:W, 55, pages 493-513.

Noun

1. Template:Lb A type of correspondence between partially ordered sets (posets), also applicable to preordered sets.
   • 1986, Horst Herrlich, Miroslav Hušek, Galois Connections, Austin Melton, Mathematical Foundation of Programming Semantics: International Conference, Proceedings, Springer, Lecture Notes in Computer Science: 239, page 122,

     Define maps $G:A\to B$ and $F:B\to A$ by $G(a)=\{y\in Y|\mathrm{\forall }x\in ax\rho y\}$ and $F(b)=\{x\in X|\mathrm{\forall }y\in bx\rho y\}$. Then $(F,G)$ is called a Galois connection of the first kind.

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Hypernyms

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Hyponyms

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