Rodelo, Diana
[UCL]
Gran, Marino
[UCL]
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 Beck-Chevalley 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.
Bibliographic reference |
Rodelo, Diana ; Gran, Marino. Beck-Chevalley condition and Goursat categories. In: Journal of Pure and Applied Algebra, Vol. 221, no. 10, p. 2245-2457 (October 2017) |
Permanent URL |
http://hdl.handle.net/2078.1/179668 |