The Stacks project

Situation 48.16.1. Here $S$ is a Noetherian scheme and $\textit{FTS}_ S$ is the category whose

1. objects are schemes $X$ over $S$ such that the structure morphism $X \to S$ is both separated and of finite type, and

2. morphisms $f : X \to Y$ between objects are morphisms of schemes over $S$.