Lemma 29.53.5. Let

be a commutative diagram of morphisms of schemes. Assume $f_1$, $f_2$ quasi-compact and quasi-separated. Let $f_ i = \nu _ i \circ f_ i'$, $i = 1, 2$ be the canonical factorizations, where $\nu _ i : X_ i' \to X_ i$ is the normalization of $X_ i$ in $Y_ i$. Then there exists a unique arrow $X'_2 \to X'_1$ fitting into a commutative diagram

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