The Beck-Chevalley property for Goursat categories

Description:  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. We then prove that the reflector to any (regular epi)-reflective subcategory of a regular Goursat category preserves pullbacks of split epimorphisms. This implies that the so-called internal Galois pregroupoid of an extension is an internal groupoid. Date:  2016-03-22 Start Time:   15:30 Speaker:  Diana Rodelo (CMUC, Univ. Algarve) Institution:  CMUC, Univ. Algarve Place:  Sala 5.5 Research Groups: -Algebra, Logic and Topology See more:   <Main>