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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