Geodesic
The Ursini commutator as normalized Smith-Pedicchio commutator
Theory and applications of categories, CT2011, Tome 27 (2012), pp. 174-188

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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},
     journal = {Theory and applications of categories},
     pages = {174--188},
     publisher = {mathdoc},
     volume = {27},
     year = {2012},
     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/