Definition 52.16.7. In Situation 52.16.1 let $(\mathcal{F}_ n)$ be an object of $\textit{Coh}(U, I\mathcal{O}_ U)$. We say $(\mathcal{F}_ n)$ canonically extends to $X$ if the the inverse system

$\{ \widetilde{H^0(U, \mathcal{F}_ n)}\} _{n \geq 1}$

in $\mathit{QCoh}(\mathcal{O}_ X)$ is pro-isomorphic to an object $(\mathcal{G}_ n)$ of $\textit{Coh}(X, I\mathcal{O}_ X)$.

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