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Internal profunctors and commutator theory; applications to extensions classification and categorical Galois Theory
Theory and applications of categories, Tome 24 (2010), pp. 451-488
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We clarify the relationship between internal profunctors and connectors on pairs (R,S) of equivalence relations which originally appeared in our new profunctorial approach of the Schreier-Mac Lane extension theorem. This clarification allows us to extend this Schreier-Mac Lane theorem to any exact Mal'cev category with centralizers. On the other hand, still in the Mal'cev context and in respect to the categorical Galois theory associated with a reflection I, it allows us to produce the faithful action of a certain abelian group on the set of classes (up to isomorphism) of I-normal extensions having a given Galois groupoid.

Classification : 18G50, 18D35, 18B40, 20J15, 08C05
Keywords: Mal'cev categories, centralizers, profunctor, Schreier-Mac Lane extension theorem, internal groupoid, Galois groupoid 
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     author = {Dominique Bourn},
     title = {Internal profunctors and commutator theory; 
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     journal = {Theory and applications of categories},
     pages = {451--488},
     year = {2010},
     volume = {24},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2010_24_a16/}
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Dominique Bourn. Internal profunctors and commutator theory; 
applications to extensions classification and categorical Galois Theory. Theory and applications of categories, Tome 24 (2010), pp. 451-488. http://geodesic.mathdoc.fr/item/TAC_2010_24_a16/