Definition 18.8.1. Let $f, g : (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}_\mathcal {C}) \to (\mathop{\mathit{Sh}}\nolimits (\mathcal{D}), \mathcal{O}_\mathcal {D})$ be two morphisms of ringed topoi. A *2-morphism from $f$ to $g$* is given by a transformation of functors $t : f_* \to g_*$ such that

is commutative.

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