The Stacks project

Lemma 4.35.15. Let $p : \mathcal{S} \to \mathcal{C}$ be a category fibred in groupoids. Let $x \to y$ and $z \to y$ be morphisms of $\mathcal{S}$. If $p(x) \times _{p(y)} p(z)$ exists, then $x \times _ y z$ exists and $p(x \times _ y z) = p(x) \times _{p(y)} p(z)$.

Proof. Follows from Lemma 4.33.13. $\square$

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