The Stacks project

Remark 68.17.10. An informal description of the properties $(\beta )$, decent, reasonable, very reasonable was given in Section 68.6. A morphism has one of these properties if (very) loosely speaking the fibres of the morphism have the corresponding properties. Being decent is useful to prove things about specializations of points on $|X|$. Being reasonable is a bit stronger and technically quite easy to work with.

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