Lemma 15.59.12. Let $R$ be a ring. Let $\alpha : P^\bullet \to Q^\bullet $ be a quasi-isomorphism of K-flat complexes of $R$-modules. For every complex $L^\bullet $ of $R$-modules the induced map
is a quasi-isomorphism.
Lemma 15.59.12. Let $R$ be a ring. Let $\alpha : P^\bullet \to Q^\bullet $ be a quasi-isomorphism of K-flat complexes of $R$-modules. For every complex $L^\bullet $ of $R$-modules the induced map
is a quasi-isomorphism.
Proof. Choose a quasi-isomorphism $K^\bullet \to L^\bullet $ with $K^\bullet $ a K-flat complex, see Lemma 15.59.10. Consider the commutative diagram
The result follows as by Lemma 15.59.2 the vertical arrows and the top horizontal arrow are quasi-isomorphisms. $\square$
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