Let be a duality of for . If is composed with the natural isomorphism between and , the composition is an incidence preserving bijection between and . By the Fundamental theorem of projective geometry is induced by a semilinear map with associated isomorphism , which can be viewed as an antiautomorphism of . In the classical literature, would be called a reciprocity in general, and if it would be called a correlation (and would necessarily be a field). Some authors suppress the role of the natural isomorphism and call a duality. When this is done, a duality may be thought of as a collineation between a pair of specially related projective spaces and called a reciprocity. If this collineation is a projectivity then it is called a correlation.