Proposition 7.14.7. Let $\mathcal{C}$ and $\mathcal{D}$ be sites. Let $u : \mathcal{C} \to \mathcal{D}$ be continuous. Assume furthermore the following:

the category $\mathcal{C}$ has a final object $X$ and $u(X)$ is a final object of $\mathcal{D}$ , and

the category $\mathcal{C}$ has fibre products and $u$ commutes with them.

Then $u$ defines a morphism of sites $\mathcal{D} \to \mathcal{C}$, in other words $u_ s$ is exact.

## Comments (1)

Comment #993 by Johan Commelin on

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