The Stacks project

Definition 21.17.13. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\mathcal{F}^\bullet $ be an object of $D(\mathcal{O})$. The derived tensor product

\[ - \otimes _\mathcal {O}^{\mathbf{L}} \mathcal{F}^\bullet : D(\mathcal{O}) \longrightarrow D(\mathcal{O}) \]

is the exact functor of triangulated categories described above.

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