Category:Definitions/Galois Connections

This category contains definitions related to Galois Connections.
Related results can be found in Category:Galois Connections.

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

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

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

$g$ and $d$ are increasing mappings and

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