The Stacks project

Definition 29.55.6. Let $f : Y \to X$ be a quasi-compact, quasi-separated, and dominant morphism of schemes.

1. The factorization $Y \to X^{Y/sn} \to X$ constructed in Lemma 29.55.5 part (2) is the seminormalization of $X$ in $Y$.

2. The factorization $Y \to X^{Y/wn} \to X$ constructed in Lemma 29.55.5 part (1) is the weak normalization of $X$ in $Y$.