Definition 20.26.2. Let $(X, \mathcal{O}_ X)$ be a ringed space. A complex $\mathcal{K}^\bullet $ of $\mathcal{O}_ X$-modules is called *K-flat* if for every acyclic complex $\mathcal{F}^\bullet $ of $\mathcal{O}_ X$-modules the complex

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

is acyclic.

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