Lemma 79.3.10. Let $S$ be a scheme. Let $a : F \to G$ and $b : G \to H$ be transformations of functors $(\mathit{Sch}/S)_{fppf}^{opp} \to \textit{Sets}$. Assume

$\Delta : G \to G \times _ H G$ is representable by algebraic spaces, and

$b \circ a : F \to H$ is representable by algebraic spaces.

Then $a$ is representable by algebraic spaces.

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