## Return to Answer

3 added 55 characters in body

I'm not sure if this is what you are looking for, but the word "natural" is often used to imply that the object being discussed is in fact a natural transformationNatural Transformation. For example, the isomorphism $V\cong V^{**}$ between a finite dimensional vector space and its double dual is natural in the sense that it is a natural isomorphism between functors. The same holds for the isomorphism $G/\mbox{Ker}\:\phi\cong H$ when $\phi:G\to H$ is a surjective homomorphism and $G,H$ are groups.

2 added 26 characters in body

I'm not sure if this is what you are looking for, but the word "natural" is often used to imply that the object being discussed is in fact a natural transformation. For example, the isomorphism $V\cong V^{**}$ between a finite dimensional vector space and its double dual is natural in the sense that it is a natural isomorphism between functors. The same holds for the isomorphism $G/\mbox{Ker}\:\phi\cong H$ when $\phi:G\to H$ is a surjective homomorphism and $G,H$ are groups.

1

I'm not sure if this is what you are looking for, but the word "natural" is often used to imply that the object being discussed is in fact a natural transformation. For example, the isomorphism $V\cong V^{**}$ between a vector space and its dual is natural in the sense that it is a natural isomorphism between functors. The same holds for the isomorphism $G/\mbox{Ker}\:\phi\cong H$ when $\phi:G\to H$ is a surjective homomorphism and $G,H$ are groups.