The Stacks project

Lemma 4.34.3. Let $F : \mathcal{S} \to \mathcal{S}'$ be a $1$-morphism of categories fibred over a category $\mathcal{C}$. Then the diagram

\[ \xymatrix{ \mathcal{I}_{\mathcal{S}/\mathcal{S}'} \ar[d]_{F \circ (042H)} \ar[rr]_{(04Z5)} & & \mathcal{I}_\mathcal {S} \ar[d]^{(04Z4)} \\ \mathcal{S}' \ar[rr]^ e & & \mathcal{I}_{\mathcal{S}'} } \]

is a $2$-fibre product.

Proof. Omitted. $\square$

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