Facets of congruence distributivity in Goursat categories

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...

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Bibliographic Details
Main Author: Gran, Marino (author)
Other Authors: Rodelo, Diana (author), Nguefeu, Idriss Tchoffo (author)
Format: article
Language:eng
Published: 2022
Subjects:
Mal'tsev categories
Goursat categories
Congruence distributive varieties
Shifting Lemma
Triangular Lemma
Trapezoid Lemma
Mathematics
Online Access:http://hdl.handle.net/10400.1/16380
Country:Portugal
Oai:oai:sapientia.ualg.pt:10400.1/16380
Description
Summary: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. (C) 2020 Elsevier B.V. All rights reserved.

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