Having given a characterization of the categorical congruence modularity getting rid of the assumption that the ground category is regular, we give now a characterization of the categorical congruence distributivity. We have a look as well at the case where the congruence distributivity is only involved, in some sense, for a subclass $\Gamma$ of equivalence relations.
Keywords: Suprema of equivalence relations, congruence modularity, congruence distributivity
2010 MSC: 08B10, 08C05, 18A20, 18A32
Theory and Applications of Categories, Vol. 34, 2019, No. 16, pp 438-455.