Beck-Chevalley condition and Goursat categories

Gran, Marino; Rodelo, Diana

http://hdl.handle.net/10400.1/12989

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Authors

Gran, Marino

Rodelo, Diana

Abstract(s)

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.