The Stacks project

Lemma 85.27.5. Let $f : X \to S$ be a morphism of schemes. The construction

\[ \begin{matrix} \text{category of cartesian } \\ \text{schemes over } (X/S)_\bullet \end{matrix} \longrightarrow \begin{matrix} \text{ category of descent data} \\ \text{ relative to } X/S \end{matrix} \]

of Lemma 85.27.4 is an equivalence of categories.

Proof. The functor from left to right is given in Lemma 85.27.4. Hence this is a special case of Lemma 85.27.2. $\square$

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