Lemma 80.3.8. Let $S$ be a scheme. Let
be maps of presheaves on $(\mathit{Sch}/S)_{fppf}$. If $a$ and $b$ are representable by algebraic spaces, so is $b \circ a$.
Lemma 80.3.8. Let $S$ be a scheme. Let
be maps of presheaves on $(\mathit{Sch}/S)_{fppf}$. If $a$ and $b$ are representable by algebraic spaces, so is $b \circ a$.
Proof. Let $T$ be a scheme over $S$, and let $T \to H$ be a morphism. By assumption $T \times _ H G$ is an algebraic space. Hence by Lemma 80.3.7 we see that $T \times _ H F = (T \times _ H G) \times _ G F$ is an algebraic space as well. $\square$
Comments (0)