This is inspired by *The 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.