Questions tagged [galois-connections]

Let $f'\colon X \to Y$ and $P(X)$ and $P(Y)$ be the powersets of $X$ and $Y$. Let $f \colon P(X) \to P(Y)$, $f(U) = \{ y \in Y | \exists x \in U (f'(x) = y) \},$ and $f^{-1} \colon P(Y) \to P(X)$, $f^{-1}(V) = \{ x \in X | \exists y \in V…