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.
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.
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.