Geodesic
Weighted normal commutator as the Huq commutator in points
Theory and applications of categories, Tome 35 (2020), pp. 1530-1545

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We show that the weighted normal commutator is obtained by applying the kernel functor to the Huq commutator of certain morphisms in a category of points over a fixed object. In addition, we compare the local representation (that is, an equivalence relation considered as a subobject in a category of points over a fixed object) of the Smith commutator of a pair of equivalence relations and the Huq commutator of the corresponding local representations, showing that they coincide in a normal Mal'tsev category with finite colimits.

Publié le :
Classification : 18E08, 18E13, 18A30, 18A20
Keywords: Weighted commutators, Huq commutator, Smith commutator, points 
@article{TAC_2020_35_a38,
     author = {Vaino Tuhafeni Shaumbwa},
     title = {Weighted normal commutator as the {Huq} commutator in points},
     journal = {Theory and applications of categories},
     pages = {1530--1545},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a38/}
}
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Vaino Tuhafeni Shaumbwa. Weighted normal commutator as the Huq commutator in points. Theory and applications of categories, Tome 35 (2020), pp. 1530-1545. http://geodesic.mathdoc.fr/item/TAC_2020_35_a38/