Abstract
Starting from a characterization of the so-called Shifting Lemma by a property of the fibers of the fibration ¶ of split epimorphisms in the category on the model of what happens for Mal’tsev categories, we shall investigate it in two directions: (1) a new one: in following the golden thread of the abelian split epimorphisms naturally provided by this characterization; (2) a more expected one: in measuring the distance between the consequences of the Shifting Lemma in the varietal context of congruence modular varieties and in the much more general categorical one. Along the way we shall emphasize a quite amazing phenomenon we called algebraic crystallography.
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