


The BeckChevalley 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 BeckChevalley 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 3permutable 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 socalled internal Galois pregroupoid of an extension is an internal groupoid.

Date: 
20160322

Start Time: 
15:30 
Speaker: 
Diana Rodelo (CMUC, Univ. Algarve)

Institution: 
CMUC, Univ. Algarve

Place: 
Sala 5.5

Research Groups: 
Algebra, Logic and Topology

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