CatGloss

The adjective natural'' had been used colloquially by mathematicians to mean defined without arbitrary choices.’’ For instance, to define an isomorphism between a finite-dimensional vector space $V$ and its dual, the vector space of linear maps from $V$ to the ground field $\mathbbe{k}$, requires a choice of basis. However, there is an isomorphism between $V$ and its double dual that requires no choice of basis; the latter, but not the former, is \emph{natural}.