The Stacks project

Remark 56.5.3. Below we will use that for an affine morphism $h : T \to S$ we have $h_*\mathcal{G} \otimes _{\mathcal{O}_ S} \mathcal{H} = h_*(\mathcal{G} \otimes _{\mathcal{O}_ T} h^*\mathcal{H})$ for $\mathcal{G} \in \mathit{QCoh}(\mathcal{O}_ T)$ and $\mathcal{H} \in \mathit{QCoh}(\mathcal{O}_ S)$. This follows immediately on translating into algebra.