Lemma 66.48.4. Let $S$ be a scheme. Let $f : Y \to X$ be a quasi-compact and quasi-separated morphism of algebraic spaces over $S$. Let $Y \to X' \to X$ be the normalization of $X$ in $Y$.
If $W \to X$ is an étale morphism of algebraic spaces over $S$, then $W \times _ X X'$ is the normalization of $W$ in $W \times _ X Y$.
If $Y$ and $X$ are representable, then $Y'$ is representable and is canonically isomorphic to the normalization of the scheme $X$ in the scheme $Y$ as constructed in Morphisms, Section 29.54.