The Stacks project

Definition 52.16.5. In Situation 52.16.1 let $(\mathcal{F}_ n)$ be an object of $\textit{Coh}(U, I\mathcal{O}_ U)$. We say $(\mathcal{F}_ n)$ extends to $X$ if there exists an object $(\mathcal{G}_ n)$ of $\textit{Coh}(X, I\mathcal{O}_ X)$ whose restriction to $U$ is isomorphic to $(\mathcal{F}_ n)$.