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Exercise 2.2.ii. Explain why the Yoneda lemma does not dualize to classify natural transformations from an arbitrary set-valued functor to a represented functor.

I don't understand the meaning that "Yoneda lemma does not dualize to classify natural transformations"; Could you explain what it means?

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She's asking you to say why the Yoneda lemma does not imply that there is a natural bijection $$\mathrm{Hom}(F,\mathsf{C}(c,-)) \cong Fc$$ for a functor $F : \mathsf{C} \to \mathbf{Set}$ and an object $c$ of $\mathsf{C}$.

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    $\begingroup$ Thank you very much! Now I understand! $\endgroup$ – user124697 Aug 6 '19 at 2:05

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