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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.
@article{TAC_2010_24_a16,
author = {Dominique Bourn},
title = {Internal profunctors and commutator theory;
applications to extensions classification and categorical {Galois} {Theory}},
journal = {Theory and applications of categories},
pages = {451--488},
publisher = {mathdoc},
volume = {24},
year = {2010},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2010_24_a16/}
}
TY - JOUR AU - Dominique Bourn TI - Internal profunctors and commutator theory; applications to extensions classification and categorical Galois Theory JO - Theory and applications of categories PY - 2010 SP - 451 EP - 488 VL - 24 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2010_24_a16/ LA - en ID - TAC_2010_24_a16 ER -
%0 Journal Article %A Dominique Bourn %T Internal profunctors and commutator theory; applications to extensions classification and categorical Galois Theory %J Theory and applications of categories %D 2010 %P 451-488 %V 24 %I mathdoc %U http://geodesic.mathdoc.fr/item/TAC_2010_24_a16/ %G en %F TAC_2010_24_a16
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/