2021/03/23 by Dominique Bourn, Bourn, Dominique
Mathematics · #08A30 #08B05 #18A20 #18C10 #18C40 #18E13 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:08A30 #msc:08B05 #msc:18A20 #msc:18C10 #msc:18C40 #msc:18E13
paper · pdf · doi:10.48550/arxiv.2103.12387
48 pages
arxiv created 2021/03/23 · arxiv updated 2021/03/24
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 ¶\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.