Polymorphism of a relation

Summary

An operation $f \colon A^n \to A$ is a polymorphism of a relation $R \subseteq A^m$ when applying $f$ coordinatewise to tuples of $R$ always gives a tuple of $R$. One also says that $f$ preserves $R$, or that $R$ is invariant under $f$. The polymorphisms of a set of relations form a clone, and this links operations to relations through a Galois connection. Polymorphisms are the main tool of the algebraic approach to constraint satisfaction problems.