Beck-Chevalley condition and Goursat categories
(2017) Journal of Pure and Applied Algebra — Vol. 221, n° 10, p. 2245-2457 (2017)
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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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Rodelo, D., & Gran, M. (2017). Beck-Chevalley condition and Goursat categories. Journal of Pure and Applied Algebra, 221(10), 2245-2457. https://hdl.handle.net/2078.5/58096 (Original work published 2017)