This is inspired by [*The Whitehead for maps*](https://mathoverflow.net/questions/2672/whitehead-for-maps) question.


Consider two maps `f, g: X\to Y` which happen to induce the same maps (of discrete spaces) `[Z, X] \to [Z, Y]` for every Z. Does this mean `f` and `g` are homotopic?


And what would be the lessons from the answer to this question? I feel like there's something interesting about the way we should ask it.



Something like Yoneda's lemma
Yes, this is a special case of Yoneda. Let Z=X and consider the identity map in [X,X]; the hypothesis says that f1=f and g1=g are then equal as elements of [X,Y].


