This is inspired by [*The Whitehead for maps*][1] 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.


  [1]: http://mathoverflow.net/questions/2672/whitehead-for-maps