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Messed up the primes
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aisejohan committed May 17, 2018
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Expand Up @@ -2629,13 +2629,13 @@ \section{Restriction and quotient stacks}
$$
[f] : [U/R] \longrightarrow [U'/R']
$$
is fully faithful if and only if $R'$ is the restriction of
$R$ via the morphism $f : U \to U'$.
is fully faithful if and only if $R$ is the restriction of
$R'$ via the morphism $f : U \to U'$.
\end{lemma}

\begin{proof}
Let $x, y$ be objects of $[U/R]$ over a scheme $T/S$.
Let $x', y'$ be the images of $x, y$ in the category $[U'/'R]_T$.
Let $x', y'$ be the images of $x, y$ in the category $[U'/R']_T$.
The functor $[f]$ is fully faithful if and only if the map of sheaves
$$
\mathit{Isom}(x, y) \longrightarrow \mathit{Isom}(x', y')
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