Galois connections

A Galois connection is a mathematical relationship between two ordered sets that links their elements through two related functions, called maps. Think of it as a way to connect properties and structure between different systems—when one element in the first set corresponds to an element in the second, the two maps preserve certain orderings and relationships. This concept helps formalize how different mathematical structures relate, such as linking solutions of equations to their parameters, ensuring that the structure of one set reflects and is compatible with that of the other.