Variations of the Shifting Lemma and Goursat categories (Preprint)

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Type: Preprint
National /International: International
Title: Variations of the Shifting Lemma and Goursat categories
Publication Date: 2018-09-26
Authors: - Marino Gran
- Diana Rodelo
- Idriss Tchoffo Nguefeu
Abstract: We prove that Mal’tsev and Goursat categories may be characterised through stronger variations of the Shifting Lemma, that is classically expressed in terms of three congruences R, S and T, and characterises congruence modular varieties. We first show that a regular category is a Mal’tsev category if and only if the Shifting Lemma holds for reflexive relations on the same object in C. Moreover, we prove that a regular category C is a Goursat category if and only if the Shifting Lemma holds for a reflexive relation S and reflexive and positive relations R and T in C. In particular this provides a new characterisation of 2-permutable and 3-permutable varieties and quasi-varieties of universal algebras.
Institution: DMUC 18-38
Online version: http://www.mat.uc.pt...prints/eng_2018.html
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