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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