  The aim of this work is to point out a strong structural phenomenon hidden
behind the existence of normalizers through the investigation of this property
in the non-pointed context: given any category E, a certain property of the
fibration of points: Pt(E) --> E guarentees the existence of normalizers. This
property becomes a characterization of this existence when E is quasi-pointed
and protomodular. This property is also showed to be equivalent to a property
of the category GrdE of internal groupoids in E which is a kind of opposite,
for the monomorphic internal functors, of the comprehensive factorization.
