Lemma 7.42.6. Let $f : \mathcal{D} \to \mathcal{C}$ be a morphism of sites associated to the continuous functor $u : \mathcal{C} \to \mathcal{D}$. If $u$ is almost cocontinuous then $f_*$ commutes with pushouts and coequalizers (and more generally finite connected colimits).

**Proof.**
This is a special case of Lemma 7.42.5.
$\square$

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