Gran, MarinoRodelo, Diana2019-11-202019-11-202017-100022-4049http://hdl.handle.net/10400.1/12989We 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.engMalcev categoriesGoursat categories3-permutable varietiesShifting LemmaBeck-Chevalley conditionReflective subcategoriesGalois groupoidBeck-Chevalley condition and Goursat categoriesjournal article10.1016/j.jpaa.2016.12.031