BeckChevalley condition and Goursat categories
Abstract
We characterise regular Goursat categories through a specific stability property of regular epimorphisms with respect to pullbacks. Under the assumption of the existence of some pushouts this property can be also expressed as a restricted BeckChevalley condition, with respect to the fibration of points, for a special class of commutative squares. In the case of varieties of universal algebras these results give, in particular, a structural explanation of the existence of the ternary operations characterising $3$permutable varieties of universal algebras.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 DOI:
 10.48550/arXiv.1512.04066
 arXiv:
 arXiv:1512.04066
 Bibcode:
 2015arXiv151204066G
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Rings and Algebras;
 08C05;
 08B05;
 18C05;
 18B99;
 18E10
 EPrint:
 Revised version: the proof of Theorem 1.3 has been changed. The paper is going to be published in the Journal of Pure and Applied Algebra