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Small changes in spaces-simplicial
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aisejohan committed Feb 27, 2017
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Expand Up @@ -5488,12 +5488,12 @@ \section{Proper hypercoverings in topology}

\begin{proof}
Write $\Sh(X) = \Sh(X_{Zar})$. Observe that both
$(\textit{LC}_{qc}/U)_{total})$ and $U_{Zar}$ fall
$(\textit{LC}_{qc}/U)_{total}$ and $U_{Zar}$ fall
into case A of Situation \ref{situation-simplicial-site}.
This is immediate from the construction of
$U_{Zar}$ in Section \ref{section-simplicial-top}
and it follows from Lemma \ref{lemma-sr-when-fibre-products}
for $(\textit{LC}_{qc}/U)_{total})$.
for $(\textit{LC}_{qc}/U)_{total}$.
Next, consider the functors
$U_{n, Zar} \to \textit{LC}_{qc}/U_n$, $U \mapsto U/U_n$
and
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