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The Stacks project

Definition 96.4.5. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. We denote

\[ f = (f^{-1}, f_*) : \mathop{\mathit{Sh}}\nolimits (\mathcal{X}_{fppf}) \longrightarrow \mathop{\mathit{Sh}}\nolimits (\mathcal{Y}_{fppf}) \]

the associated morphism of fppf topoi constructed above. Similarly for the associated Zariski, étale, smooth, and syntomic topoi.

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