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
Famous quotes containing the word connection:
“Accept the place the divine providence has found for you, the society of your contemporaries, the connection of events.”
—Ralph Waldo Emerson (1803–1882)