 Many kinds of objects are characterized by what structure their maps hold invariant. Posets transform via monotone functions, leaving order invariant. Algebras transform via homomorphisms, leaving the algebraic structure invariant. In algebraic geometry varieties transform via regular \(n\)-ary functions \(f: A^n \rightarrow A\), defined as functions that are locally rational polynomials in \(n\) variables. Locally rational means that at each point of the domain of \(f\) there exists a neighborhood on which \(f\) is the ratio of two polynomials, the denominator of which is nonzero in that neighborhood.