Twisted Commutators and Internal Crossed Modules

Deval, Bo Shan;Van der Linden, Tim
(2024) Advanced Studies: Euro-Tbilisi Mathematical Journal — Vol. 17, n° 3, p. 25-52 (2024)

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Abstract
We introduce a notion of relative commutator -- an important special case being commutators twisted by an action -- as a straightforward modification of the definition of the Higgins commutator, establish its relation with a new notion of commutativity -- also obtained as a modification of the usual notion -- and show how we can use it to characterise internal crossed modules in the context of a semi-abelian category.
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Deval, B. S., & Van der Linden, T. (2024). Twisted Commutators and Internal Crossed Modules. Advanced Studies: Euro-Tbilisi Mathematical Journal, 17(3), 25-52. https://doi.org/10.32513/asetmj/1932200824027 (Original work published 2024)