  In a semi-abelian context, we study the condition (NH) asking that Higgins
commutators of normal subobjects are normal subobjects. We provide examples of
categories that do or do not satisfy this property. We focus on the
relationship with the "Smith is Huq" condition (SH) and characterise those
semi-abelian categories in which both (NH) and (SH) hold in terms of reflection
and preservation properties of the change of base functors of the fibration of
points.
