Facets of congruence distributivity in Goursat categories
arXiv:1909.10211 · doi:10.1016/j.jpaa.2020.106380
Abstract
We 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 -permutable varieties) through variations of the Triangular and Trapezoid Lemmas involving reflexive and positive relations.
21 pages