Definition 21.17.2. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. A complex $\mathcal{K}^\bullet $ of $\mathcal{O}$-modules is called *K-flat* if for every acyclic complex $\mathcal{F}^\bullet $ of $\mathcal{O}$-modules the complex

\[ \text{Tot}(\mathcal{F}^\bullet \otimes _\mathcal {O} \mathcal{K}^\bullet ) \]

is acyclic.

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