Example 59.9.2. Given an object $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$, we consider the rule

This defines a functor $h_ X : \mathcal{C}^{opp} \to \textit{Sets}$ and hence a presheaf. This is called the *representable presheaf associated to $X$.* It is not true that representable presheaves are sheaves in every topology on every site.

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