 Locally of finite type

A morphism of schemes $f:X\to S$ is locally of finite type if, over every affine open subscheme $\mathrm{Spec}A\subseteq S$, its inverse image is covered by affine schemes $\mathrm{Spec}B$ with $B$ a finitely generated $A$-algebra. It is of finite type exactly when it is also a quasi-compact morphism.