Lemma 94.6.1 (02ZR)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 94: Algebraic Stacks
Section 94.6: Representable morphisms of categories fibred in groupoids
Lemma 94.6.1 (cite)

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Lemma 94.6.1. Let $f : X \to Y$ be a morphism of $(\mathit{Sch}/S)_{fppf}$. Then the $1$-morphism induced by $f$

\[ (\mathit{Sch}/X)_{fppf} \longrightarrow (\mathit{Sch}/Y)_{fppf} \]

is a representable $1$-morphism.

Proof. This is formal and relies only on the fact that the category $(\mathit{Sch}/S)_{fppf}$ has fibre products. $\square$

Comments (2)

Comment #7706 by Mingchen on August 26, 2022 at 03:01

You might want to say that $f:X\rightarrow Y$ is a morphism over $S$ ?

Comment #7966 by Stacks Project on January 12, 2023 at 13:56

Thanks and fixed here.

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