Well-pointed object in a category
= Well-pointed object in a category
= Well-pointed objects in a category
{synonym}
An object $A$ in a category with a <terminal object> is well-pointed when every <monomorphism> $m:B\to A$ through which all points $1\to A$ factor is invertible. This definition concerns detection of proper subobjects by points, and does not designate a chosen basepoint. If there are no points, it asserts that every subobject is the whole object. In particular, the empty set is well-pointed.