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sav08:galois_connection_on_lattices [2008/05/07 10:03] vkuncak |
sav08:galois_connection_on_lattices [2008/05/07 10:03] vkuncak |
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==== Galois Connection ==== | ==== Galois Connection ==== | ||
- | Galois connection is defined by two monotonic functions $\alpha : C \to A$ and $\gamma : A \to C$ between [[partial order]]s $\leq$ on $C$ and $\sqsubseteq$ on $A$, such that | + | Galois connection is defined by two monotonic functions $\alpha : C \to A$ and $\gamma : A \to C$ between [[:partial order]]s $\leq$ on $C$ and $\sqsubseteq$ on $A$, such that |
\begin{equation*} | \begin{equation*} | ||
\alpha(c) \sqsubseteq a\ \iff\ c \leq \gamma(a) \qquad (*) | \alpha(c) \sqsubseteq a\ \iff\ c \leq \gamma(a) \qquad (*) |