\begin{definition}[Definition:Galois Connection]
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''' {{iff}}:
:$g$ 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.
{{definition wanted|monotone, antitone, closure operator, closed}}
{{NamedforDef|Évariste Galois|cat = Galois}}
\end{definition}