Remark 29.49.14. There is a variant of Definition 29.49.1 where we consider only those morphism $U \to Y$ defined on scheme theoretically dense open subschemes $U \subset X$. We use Lemma 29.7.6 to see that we obtain an equivalence relation. An equivalence class of these is called a pseudo-morphism from $X$ to $Y$. If $X$ is reduced the two notions coincide.
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