Remark 7.14.9. (Skip on first reading.) Let $\mathcal{C}$ and $\mathcal{D}$ be sites. Analogously to Definition 7.14.1 we say that a *quasi-morphism of sites $f : \mathcal{D} \to \mathcal{C}$* is given by a quasi-continuous functor $u : \mathcal{C} \to \mathcal{D}$ (see Remark 7.13.6) such that $u_ s$ is exact. The analogue of Proposition 7.14.7 in this setting is obtained by replacing the word “continuous” by the word “quasi-continuous”, and replacing the word “morphism” by “quasi-morphism”. The proof is literally the same.

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