# Something like Yoneda's lemma

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.

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I found it myself: the image of id \in [X, X] under both maps will be the same class in [X, Y], which is the definition of homotopy between f and g, so the ansewr is yes.