The Stacks project

Lemma 65.3.3. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$. Let $F, G, H : (\mathit{Sch}/S)_{fppf}^{opp} \to \textit{Sets}$. Let $a : F \to G$ be a representable transformation of functors. Let $b : H \to G$ be any transformation of functors. Consider the fibre product diagram

\[ \xymatrix{ H \times _{b, G, a} F \ar[r]_-{b'} \ar[d]_{a'} & F \ar[d]^ a \\ H \ar[r]^ b & G } \]

Then the base change $a'$ is a representable transformation of functors.

Proof. This is entirely formal and works in any category. $\square$

Comments (1)

Comment #1790 by Matthieu Romagny on

typo : transformations --> transformation

There are also:

  • 2 comment(s) on Section 65.3: Representable morphisms of presheaves

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