Geodesic
The Ursini commutator as normalized Smith-Pedicchio commutator
Theory and applications of categories, CT2011, Tome 27 (2012), pp. 174-188
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We introduce an intrinsic description of the Ursini commutator in any ideal determined category and we compare it with the Higgins and Huq commutators. After describing also the Smith-Pedicchio commutator by means of canonical arrows from a coproduct, we compare the two notions, showing that in any exact Mal'tsev normal category the Ursini commutator $[H,K]_{U}$ of two subobjects $H, K$ of $A$ is the normalization of the Smith-Pedicchio commutator of the equivalence relations generated by $H$ and $K$, extending the result valid for ideal determined varieties given by Ursini and Gumm.

Publié le :
Classification : 18C05, 08A30
Keywords: commutator, ideal determined category, exact Mal'tsev category 
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     author = {Sandra Mantovani},
     title = {The {Ursini} commutator as normalized {Smith-Pedicchio} commutator},
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     year = {2012},
     volume = {27},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_27_a7/}
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Sandra Mantovani. The Ursini commutator as normalized Smith-Pedicchio commutator. Theory and applications of categories, CT2011, Tome 27 (2012), pp. 174-188. http://geodesic.mathdoc.fr/item/TAC_2012_27_a7/