Definition:Galois Connection

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Let $\struct {S, \preceq}$ and $\struct {T, \precsim}$ be ordered sets.

Let $g: S \to T$, $d: T \to S$ be mappings.

Then $\struct {g, d}$ is a Galois connection if and only if:

$g$ and $d$ are increasing mappings and
$\forall s \in S, t \in T: t \precsim \map g s \iff \map d t \preceq s$

$g$ is upper adjoint and $d$ is lower adjoint of a Galois connection.

Source of Name

This entry was named for Évariste Galois.