The Stacks project

Definition 64.5.1. With $S$, and $a : F \to G$ representable as above. Let $\mathcal{P}$ be a property of morphisms of schemes which

  1. is preserved under any base change, see Schemes, Definition 26.18.3, and

  2. is fppf local on the base, see Descent, Definition 35.22.1.

In this case we say that $a$ has property $\mathcal{P}$ if for every $U \in \mathop{\mathrm{Ob}}\nolimits ((\mathit{Sch}/S)_{fppf})$ and any $\xi \in G(U)$ the resulting morphism of schemes $V_\xi \to U$ has property $\mathcal{P}$.

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