SKB is not algebraically coherent

2026/07/30 by Andrea Sciandra, Vito Volpe
Mathematics · #math.CT #math.QA #math.RA #math.RT

paper · pdf

9 pages

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We prove that the category SKB is not algebraically coherent. As a consequence, it is not locally algebraically cartesian closed. Then the same can be deduced for cocommutative Hopf braces.

Citations

• Analogs of the lower and upper central series in skew braces: a survey
• Hopf braces and semi-abelian categories
• Hopf formulae for homology of skew braces
• Split epimorphims and Baer sums of left skew braces
• Aspects of the Category SKB of Skew Braces
• Aspects of algebraic exponentiation
• The cohomological comparison arising from the associated abelian object
• Exact Categories
• COMMUTATOR, NILPOTENCY, AND SOLVABILITY IN CATEGORIES

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