Definition 7.29.2. Let $\mathcal{C}$, $\mathcal{D}$ be sites. A *special cocontinuous functor $u$ from $\mathcal{C}$ to $\mathcal{D}$* is a cocontinuous functor $u : \mathcal{C} \to \mathcal{D}$ satisfying the assumptions and conclusions of Lemma 7.29.1.

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