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lim ---> colim
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aisejohan committed Jul 28, 2017
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Expand Up @@ -2890,7 +2890,7 @@ \section{Extending quasi-coherent sheaves}
\label{lemma-finite-directed-colimit-surjective-maps}
Let $X$ be a scheme. Assume $X$ is quasi-compact and quasi-separated.
Let $\mathcal{F}$ be a finite type quasi-coherent $\mathcal{O}_X$-module.
Then we can write $\mathcal{F} = \lim \mathcal{F}_i$ with $\mathcal{F}_i$
Then we can write $\mathcal{F} = \colim \mathcal{F}_i$ with $\mathcal{F}_i$
of finite presentation and all transition maps
$\mathcal{F}_i \to \mathcal{F}_{i'}$ surjective.
\end{lemma}
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