Categorical aspects of congruence distributivity

Michael Hoefnagel and Diana Rodelo

We study a categorical condition on relations, which is a categorical formulation of Jónsson's characterisation of congruence distributive varieties. Categories satisfying these conditions need not be varieties; for instance, the dual of the categories of topological spaces, ordered sets, G-sets, and the dual of any (pre)topos all provide us with examples.

Keywords: Congruence distributivity, n-permutability, Mal'tsev condition, regular category, trapezoid lemma, majority category

2020 MSC: 08B05, 08B10, 18E08, 18E13

Theory and Applications of Categories, Vol. 41, 2024, No. 17, pp 531-550.

Published 2024-05-22.

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