$\mathsf{SKB}$ is not algebraically coherent

Andrea Sciandra; Vito Volpe

$\mathsf{SKB}$ is not algebraically coherent

Category Theory 2026-07-30 v1 Quantum Algebra Rings and Algebras Representation Theory

Authors: Andrea Sciandra , Vito Volpe

Abstract

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

Cite

@article{arxiv.2607.28380,
  title  = {$\mathsf{SKB}$ is not algebraically coherent},
  author = {Andrea Sciandra and Vito Volpe},
  journal= {arXiv preprint arXiv:2607.28380},
  year   = {2026}
}

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9 pages