Lemma 61.17.1. Let $S$ be a scheme. Let $T$ be an object of $(\mathit{Sch}/S)_{pro\text{-}\acute{e}tale}$.

If $\mathcal{I}$ is injective in $\textit{Ab}((\mathit{Sch}/S)_{pro\text{-}\acute{e}tale})$, then

$i_ f^{-1}\mathcal{I}$ is injective in $\textit{Ab}(T_{pro\text{-}\acute{e}tale})$,

$\mathcal{I}|_{S_{pro\text{-}\acute{e}tale}}$ is injective in $\textit{Ab}(S_{pro\text{-}\acute{e}tale})$,

If $\mathcal{I}^\bullet $ is a K-injective complex in $\textit{Ab}((\mathit{Sch}/S)_{pro\text{-}\acute{e}tale})$, then

$i_ f^{-1}\mathcal{I}^\bullet $ is a K-injective complex in $\textit{Ab}(T_{pro\text{-}\acute{e}tale})$,

$\mathcal{I}^\bullet |_{S_{pro\text{-}\acute{e}tale}}$ is a K-injective complex in $\textit{Ab}(S_{pro\text{-}\acute{e}tale})$,

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