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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...
Protolocalisations of homological categories
Borceux, Francis; Clementino, Maria Manuel; Gran, Marino; Sousa, LurdesA protolocalisation of a homological (resp. semi-abelian) category is a regular full reflective subcategory, whose reflection preserves short exact sequences. We study the closure operator and the torsion theory associated with such a situation. We pay special attention to the fibered, the regular epireflective and the monoreflective cases. We give examples in algebra, topos theory and functional analysis. ; ...
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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