The Stacks project

Definition 29.14.2. Let $P$ be a property of ring maps. Let $f : X \to S$ be a morphism of schemes. We say $f$ is locally of type $P$ if for any $x \in X$ there exists an affine open neighbourhood $U$ of $x$ in $X$ which maps into an affine open $V \subset S$ such that the induced ring map $\mathcal{O}_ S(V) \to \mathcal{O}_ X(U)$ has property $P$.