Gran, MarinoRodelo, DianaNguefeu, Idriss Tchoffo2021-06-242022-03-012020-100022-4049http://hdl.handle.net/10400.1/16380We 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.engMal'tsev categoriesGoursat categoriesCongruence distributive varietiesShifting LemmaTriangular LemmaTrapezoid LemmaMathematicsjournal article10.1016/j.jpaa.2020.106380