Galois connection
Every partially ordered set can be viewed as a category (where the elements of the poset become the category's objects and we have a single morphism from "x" to "y" if and only if "x" ≤ "y"). A pair of adjoint functors between two partially ordered sets is called a Galois connection (or, if it is contravariant, an "antitone" Galois connection). See that article for a number of examples: the case of Galois theory of course is a leading one. Any Galois connection gives rise to closure operators and to inverse order-preserving bijections between the corresponding closed elements.