Lemma 37.13.13. Consider a cartesian diagram of schemes

If $Y' \to Y$ is flat, then the canonical map $(g')^*\mathop{N\! L}\nolimits _{X/Y} \to \mathop{N\! L}\nolimits _{X'/Y'}$ is a quasi-isomorphism.

Lemma 37.13.13. Consider a cartesian diagram of schemes

\[ \xymatrix{ X' \ar[d] \ar[r]_{g'} & X \ar[d] \\ Y' \ar[r] & Y } \]

If $Y' \to Y$ is flat, then the canonical map $(g')^*\mathop{N\! L}\nolimits _{X/Y} \to \mathop{N\! L}\nolimits _{X'/Y'}$ is a quasi-isomorphism.

**Proof.**
By Lemma 37.13.2 this follows from Algebra, Lemma 10.133.8.
$\square$

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