But \\(f: 2^X \rightarrow 2^Y\\) and \\(g: 2^Y \rightarrow 2^X\\) are not just any pair of order-reversing functions, they have an additional property which classifies them as a **Galois connection**:

\\[f(x) \supseteq y \iff x \subseteq g(y)\\]

Using Willerton's language, these are equivalent because they both state that the objects in \\(x\\) have all the attributes in \\(y\\).

\\[f(x) \supseteq y \iff x \subseteq g(y)\\]

Using Willerton's language, these are equivalent because they both state that the objects in \\(x\\) have all the attributes in \\(y\\).