Page "Natural transformation" Paragraph 17

Every finite-dimensional vector space is isomorphic to its dual space, but this isomorphism relies on an arbitrary choice of isomorphism ( for example, via choosing a basis and then taking the isomorphism sending this basis to the corresponding dual basis ).

There is in general no natural isomorphism between a finite-dimensional vector space and its dual space.

However, related categories ( with additional structure and restrictions on the maps ) do have a natural isomorphism, as described below.