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On the category of Hopf braces
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Hopf braces are the quantum analogues of skew braces and, as such, their cocommutative counterparts provide solutions to the quantum Yang-Baxter equation. We investigate various properties of categories related to Hopf braces. In particular, we prove that the category of Hopf braces is accessible while the category of cocommutative Hopf braces is even locally presentable. We also show that functors forgetting multiple antipodes and/or multiplications down to coalgebras are monadic. Colimits in the category of cocommutative Hopf braces are described explicitly and a free cocommutative Hopf brace on an arbitrary cocommutative Hopf algebra is constructed.
Forward citations
Cited by 2 Pith papers
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A Syntactic Approach to Ulmer's Bialgebras
A syntactic framework of signature pairs and bialgebraic theories constructs internal bialgebra objects via PIE limits and lifts accessibility, presentability, regularity, and exactness.
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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.
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