Intersection of subobjects
= Intersection of subobjects
{title2=$\bigcap_iM_i$}
In a <complete category>, the intersection of a set-indexed family of <subobjects> of $C$ is their wide <pullback in a category> over $C$. The resulting morphism into $C$ is a <monomorphism>, and it factors through every member. In a <well-powered category>, even the intersection of all subobjects satisfying a specified property is small.