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- Beck-Chevalley condition and Goursat categoriesPublication . Gran, Marino; Rodelo, DianaWe characterise regular Goursat categories through a specific stability property of regular epimorphisms with respect to pullbacks. Under the assumption of the existence of some pushouts this property can be also expressed as a restricted Beck Chevalley condition, with respect to the fibration of points, for a special class of commutative squares. In the case of varieties of universal algebras these results give, in particular, a structural explanation of the existence of the ternary operations characterising 3-permutable varieties of universal algebras.
- Facets of congruence distributivity in Goursat categoriesPublication . Gran, Marino; Rodelo, Diana; Nguefeu, Idriss TchoffoWe give new characterisations of regular Mal'tsev categories with distributive lattice of equivalence relations through variations of the so-called Triangular Lemma and Trapezoid Lemma in universal algebra. We then give new characterisations of equivalence distributive Goursat categories (which extend 3-permutable varieties) through variations of the Triangular and Trapezoid Lemmas involving reflexive and positive relations. (C) 2020 Elsevier B.V. All rights reserved.