In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets). The same notion can also be defined on preordered sets or classes; this article presents the common case of posets. Galois connections generalize the correspondence between subgroups and subfields investigated in Galois theory. They find applications in various mathematical theories.
A Galois connection is rather weak compared to an order isomorphism between the involved posets, but every Galois connection gives rise to an isomorphism of certain sub-posets, as will be explained below.
Like Galois theory, Galois connections are named after the French mathematician Évariste Galois.
Read more about Galois Connection: Equivalent Definitions, Properties, Closure Operators and Galois Connections, Existence and Uniqueness of Galois Connections, Galois Connections As Morphisms, Connection To Category Theory, Applications in The Theory of Programming
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