Lemma 80.3.3. Let $S$ be a scheme. Let

be a fibre square of presheaves on $(\mathit{Sch}/S)_{fppf}$. If $a$ is representable by algebraic spaces so is $a'$.

** A base change of a representable by algebraic spaces morphism of presheaves is representable by algebraic spaces. **

Lemma 80.3.3. Let $S$ be a scheme. Let

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

be a fibre square of presheaves on $(\mathit{Sch}/S)_{fppf}$. If $a$ is representable by algebraic spaces so is $a'$.

**Proof.**
Omitted. Hint: This is formal.
$\square$

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## Comments (1)

Comment #894 by Kestutis Cesnavicius on