Lemma 75.13.10. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $L, K$ be objects of $D(\mathcal{O}_ X)$. If either

$L$ in $D^+_\mathit{QCoh}(\mathcal{O}_ X)$ and $K$ is pseudo-coherent,

$L$ in $D_\mathit{QCoh}(\mathcal{O}_ X)$ and $K$ is perfect,

then $R\mathop{\mathcal{H}\! \mathit{om}}\nolimits (K, L)$ is in $D_\mathit{QCoh}(\mathcal{O}_ X)$.

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