Weighted normal commutator as the Huq commutator in points

Vaino Tuhafeni Shaumbwa

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.

Keywords: Weighted commutators, Huq commutator, Smith commutator, points

2020 MSC: 18E08, 18E13, 18A30, 18A20

Theory and Applications of Categories, Vol. 35, 2020, No. 39, pp 1530-1545.

Published 2020-09-01.


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