The Stacks project

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

Lemma 79.3.3. 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. $\square$


Comments (1)

Comment #894 by Kestutis Cesnavicius on

Suggested slogan: A base change of a representable by algebraic spaces morphism of presheaves is representable by algebraic spaces


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