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arXiv · 1512.04066

Beck-Chevalley condition and Goursat categories

Marino Gran·Diana Rodelo
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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 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.

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Marino Gran, Diana Rodelo. 2015-12-13. Beck-Chevalley condition and Goursat categories. https://arxiv.org/abs/1512.04066

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