Separated morphism
= Separated morphism
= Separatedness
{synonym}
A morphism $f:X\to Y$ is separated when its diagonal $X\to X\times_YX$ is a <closed immersion>. This is the scheme-theoretic analogue of the Hausdorff property.
A morphism of <schemes> is separated when its diagonal is a <closed immersion>. This is a property of the morphism, distinct from the broader morphism or diagonal constructions.