We study a categorical commutator, introduced by Huq, defined for a pair of coterminal morphisms. We show that in a normal unital category C with finite colimits, the normal closure of the regular image of the Huq commutator of a pair of subobjects under an arbitrary morphism is the same as the Huq commutator of their respective regular images. Then we use this property to characterize the Huq commutator as the largest commutator satisfying certain properties.
Keywords: Commuting morphisms; Commutator; Normal, Ideal-determined, Unital category
2010 MSC: 18B30, 18A05, 18B35, 18A32
Theory and Applications of Categories, Vol. 32, 2017, No. 46, pp 1588-1600.