Support of an object in a regular category
= Support of an object in a regular category
{title2=$\sigma(A)=\operatorname{im}(A\to1)$}
The support of an object $A$ in a <regular category> is the <subterminal object> appearing as the <image of a morphism in a regular category> of $A\to1$. A <regular functor> preserves this construction. In the <Category of sets>, the support is the empty set if $A$ is empty and a singleton otherwise.