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A new characterization of Goursat categories
Gran, Marino; Rodelo, DianaWe present a new characterisation of Goursat categories in terms of special kind of pushouts, that we call Goursat pushouts. This allows one to prove that, for a regular category, the Goursat property is actually equivalent to the validity of the denormalised 3-by-3 Lemma. Goursat pushouts are also useful to clarify, from a categorical perspective, the existence of the quaternary operations characterising 3-per...
Comprehensive factorization and universal I-central extensions in the Mal'cev c...
Bourn, Dominique; Rodelo, DianaWe show that, under suitable left exact conditions on a re ection functor I, the construction of the associated universal I-central extension is reduced to the comprehensive factorization of a speci c internal functor. This observation produces some existence conditions which hold in particular for any re ection from a Mal'cev variety to any Birkho subvariety
Directions for the long exact cohomology sequence in Moore categories
Rodelo, DianaA new method for realizing the first and second order cohomology groups of an internal abelian group in a Barr-exact category was introduced in [6] and [10]. The main role, in each level, is played by a direction functor. This approach can be generalized to any level n and produces a long exact cohomology sequence. By applying this method to Moore categories we show that they represent a good context for non-ab...
The third cohomology group classifies double central extensions
Rodelo, Diana; Linden, Tim Van derWe characterise the double central extensions in a semi-abelian category in terms of commutator conditions. We prove that the third cohomology group H3(Z;A) of an object Z with coe cients in an abelian object A classi es the double central extensions of Z by A. ; FCT/Centro de Matemática da Universidade de Coimbra; Vrije Universiteit Brussel
A universal construction in Goursat categories
Gran, Marino; Rodelo, DianaWe prove that the category of internal groupoids Grd(E) is a reflective subcategory of the category Rg(E) of internal reflexive graphs in a regular Goursat category E with coequalisers: this implies that the category Grd(E) is itself regular Goursat. ; FCT; Centre of Mathematics of the University of Coimbra
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