Pith. sign in

REVIEW 2 cited by

On the category of Hopf braces

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2503.06280 v3 pith:OYUS64QT submitted 2025-03-08 math.QA math.CTmath.RA

classification math.QAmath.CTmath.RA
keywords hopfbracescocommutativecategoryquantumaccessiblealgebraanalogues
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Syntactic Approach to Ulmer's Bialgebras

    math.CT 2026-07 conditional novelty 7.0 of 10

    A syntactic framework of signature pairs and bialgebraic theories constructs internal bialgebra objects via PIE limits and lifts accessibility, presentability, regularity, and exactness.

  2. Hopf braces and semi-abelian categories

    math.RA 2024-11 accept novelty 7.0 of 10

    Cocommutative Hopf braces form a semi-abelian and strongly protomodular category, in which primitive Hopf braces and skew braces form a hereditary torsion theory.

Pith tools