Cocommutative Hopf braces form a semi-abelian and strongly protomodular category, in which primitive Hopf braces and skew braces form a hereditary torsion theory.
Barr, Exact categories, in: Springer Lecture Notes in Math
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Hopf braces and semi-abelian categories
Cocommutative Hopf braces form a semi-abelian and strongly protomodular category, in which primitive Hopf braces and skew braces form a hereditary torsion theory.