Lemma 93.9.3. Let $S$ be an object of $\mathit{Sch}_{fppf}$. Consider a $2$-commutative diagram

of $1$-morphisms of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. Assume the horizontal arrows are equivalences. Then $f$ is representable by algebraic spaces if and only if $f'$ is representable by algebraic spaces.

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