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- Some remarks on connectors and groupoids in goursat categoriesPublication . Gran, Marino; Nguefeu, Idriss Tchoffo; Rodelo, DianaWe prove that connectors are stable under quotients in any (regular) Goursat category. As a consequence, the category Conn(C) of connectors in C is a Goursat category whenever C is. This implies that Goursat categories can be characterised in terms of a simple property of internal groupoids.
- Beck-Chevalley condition and Goursat categoriesPublication . Gran, Marino; Rodelo, DianaWe 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.