  In (B-Gran, 2004), was given a categorical formulation of the Shifting Lemma
which is a characterization of the Congruence Modular Varieties among all the
variety of Universal Algebra, introduced in (Gumm, 1983).
  Starting from a characterization of this Shifting Lemma by a property of the
fibers of the fibration of points $\P\EE$ (B, 2005), on the model of what
happens for Mal'tsev categories, we shall investigate three directions:\\ 1) a
new one: in following the golden thread of abelian split epimorphisms naturally
provided by this characterization;\\ 2) a more or less expected one: in
measuring the distance between the consequences of the Shifting Lemma in the
varietal context and in the much more general categorical one;\\ 3) a quite
amazing phenomenon, which I should call Algebraic Crystallography, and which is
described in the Introduction.
