The Stacks project

Lemma 59.18.3 (Yoneda Lemma). For any presheaf $\mathcal{F}$ on a category $\mathcal{C}$ and $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$ there is a functorial isomorphism

\[ \mathop{\mathrm{Hom}}\nolimits _{\textit{PSh}(\mathcal{C})}(h_ U, \mathcal{F}) = \mathcal{F}(U). \]

Proof. See Categories, Lemma 4.3.5. $\square$

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