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On the ternary commutator, I: Exact Mal'tsev categories
Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 379-422 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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In this first article on the Bulatov commutator, we introduce a ternary commutator of equivalence relations in the context of an exact Mal'tsev category with binary coproducts. We prove that, for Mal'tsev varieties, our notion is a particular case (where n=3) of the n-fold commutator introduced (originally in the context of Mal'tsev algebras) by A. Bulatov. We study its basic stability properties as well as the relationship with the (binary) Smith-Pedicchio commutator. In a forthcoming second article, we restrict the context to algebraically coherent semi-abelian categories, where we prove that the commutator introduced here corresponds to the ternary Higgins commutator of M. Hartl and the second author.

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Classification : 18E13
Keywords: Higher commutator, exact Mal'tsev category 
@article{TAC_2021_36_a14,
     author = {Cyrille Sandry Simeu and Tim Van der Linden},
     title = {On the ternary commutator, {I:
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     journal = {Theory and applications of categories},
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     year = {2021},
     volume = {36},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_36_a14/}
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Cyrille Sandry Simeu; Tim Van der Linden. On the ternary commutator, I:
Exact Mal'tsev categories. Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 379-422. http://geodesic.mathdoc.fr/item/TAC_2021_36_a14/