<Reference List> | |
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 |
Download: | Not available |