Lemma 109.60.3. A quasi-compact and quasi-separated morphism $f : \mathcal{X} \to \mathcal{Y}$ of algebraic stacks need not induce a functor $Rf_* : D_\mathit{QCoh}(\mathcal{O}_\mathcal {X}) \to D_\mathit{QCoh}(\mathcal{O}_\mathcal {Y})$.

Proof. See discussion above. $\square$

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