Lemma 18.14.3. Let $f : (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}_\mathcal {C}) \to (\mathop{\mathit{Sh}}\nolimits (\mathcal{D}), \mathcal{O}_\mathcal {D})$ be a morphism of ringed topoi.

The functor $f_*$ is left exact. In fact it commutes with all limits.

The functor $f^*$ is right exact. In fact it commutes with all colimits.

## Comments (0)