The Stacks project

Definition 68.6.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$.

1. We say $X$ is decent if for every point $x \in X$ the equivalent conditions of Lemma 68.4.5 hold, in other words property $(\gamma )$ of Lemma 68.5.1 holds.

2. We say $X$ is reasonable if the equivalent conditions of Lemma 68.4.6 hold, in other words property $(\delta )$ of Lemma 68.5.1 holds.

3. We say $X$ is very reasonable if the equivalent conditions of Lemma 68.4.7 hold, i.e., property $(\epsilon )$ of Lemma 68.5.1 holds.