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Beck-Chevalley condition and Goursat categories
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Resumo(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.
Descrição
Palavras-chave
Malcev categories Goursat categories 3-permutable varieties Shifting Lemma Beck-Chevalley condition Reflective subcategories Galois groupoid
Contexto Educativo
Citação
Editora
Elsevier