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 3-permutable varieties) through variations of the Triangular and Trapezoid Lemmas involving reflexive and positive relations.

中文翻译：

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Goursat 类别中同余分布的方面

摘要 我们通过泛代数中所谓的三角引理和梯形引理的变体，给出了具有等价关系分布格的正则 Mal'tsev 范畴的新特征。然后，我们通过涉及自反和正关系的三角形和梯形引理的变体给出等价分配 Goursat 类别（扩展 3-置换变体）的新特征。