ABSTRACT
A Galois-connection is a connection, with certain properties, between two sets of objects, usually of different kinds. Such a connection can provide a useful tool for studying properties of one kind of object, based on the properties of the other (usually more well-known) kind of objects. In the classical Galois theory, for instance, properties of permutation groups are used to study field extensions. Such connections provide a useful tool for studying algebraic structures, and will be a main focus of study in this book. In particular, Galois-connections will be used in later chapters to produce two main examples of complete lattices of closed sets, the lattice of all varieties of a given type in Chapter 6 and the lattice of all clones on a fixed base set in Chapter 10.
