\begin{definition}[Definition:Separated Morphism of Schemes]
Let $\struct {X, \OO_X}$ and $\struct {Y, \OO_Y}$ be schemes.
Let $f : \struct {X, \OO_X} \to \struct {Y, \OO_Y}$ be a morphism of schemes.
$f$ is '''separated''' {{iff}} $f$ the diagonal morphism $\Delta_f : X \times_Y X  \to Y$ is a closed immersion.
\end{definition}