Duality (mathematics)

The following list of examples shows the common features of many dualities, but also indicates that the precise meaning of duality may vary from case to case.

The features of the cube and its dual octahedron correspond one-for-one with dimensions reversed.

in a natural way. Actually, the correspondence of limits and colimits is an example of adjoints, since there is an adjunction

In analysis, problems are frequently solved by passing to the dual description of functions and operators.

Fourier transform switches between functions on a vector space and its dual: