Geodesic
A characterization of the Huq commutator
Theory and applications of categories, Tome 32 (2017), pp. 1588-1600 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 18B30, 18A05, 18B35, 18A32
Keywords: Commuting morphisms, Commutator, Normal, Ideal-determined, Unital category 
@article{TAC_2017_32_a45,
     author = {Vaino Tuhafeni Shaumbwa},
     title = {A characterization of the {Huq} commutator},
     journal = {Theory and applications of categories},
     pages = {1588--1600},
     year = {2017},
     volume = {32},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a45/}
}
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Vaino Tuhafeni Shaumbwa. A characterization of the Huq commutator. Theory and applications of categories, Tome 32 (2017), pp. 1588-1600. http://geodesic.mathdoc.fr/item/TAC_2017_32_a45/