The Stacks project

Definition 76.44.2. Let $S$ be a scheme. Let $i : X \to Y$ be a morphism of algebraic spaces over $S$.

  1. We say $i$ is a Koszul-regular immersion if $i$ is representable and the equivalent conditions of Lemma 76.44.1 hold with $\mathcal{P}(f) =$“$f$ is a Koszul-regular immersion”.

  2. We say $i$ is an $H_1$-regular immersion if $i$ is representable and the equivalent conditions of Lemma 76.44.1 hold with $\mathcal{P}(f) =$“$f$ is an $H_1$-regular immersion”.

  3. We say $i$ is a quasi-regular immersion if $i$ is representable and the equivalent conditions of Lemma 76.44.1 hold with $\mathcal{P}(f) =$“$f$ is a quasi-regular immersion”.

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View Definition 76.44.2 as pdf