The Stacks project

Definition 29.10.1. Let $f : X \to S$ be a morphism.

1. We say that $f$ is universally injective if and only if for any morphism of schemes $S' \to S$ the base change $f' : X_{S'} \to S'$ is injective (on underlying topological spaces).

2. We say $f$ is radicial if $f$ is injective as a map of topological spaces, and for every $x \in X$ the field extension $\kappa (x)/\kappa (f(x))$ is purely inseparable.