Work

On the category of Hopf braces

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

Authors: Agore, Ana, Chirvasitu, Alexandru

Institutions: Vrije Universiteit Brussel, Max Planck Institute for Mathematics, IMAR - Institutul de Matematică „Simion Stoilow” al Academiei Române

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministerul Cercetării, Inovării şi Digitalizării, Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii, Colegiul Consultativ pentru Cercetare-Dezvoltare şi Inovare

OpenAlex ID: W6979314867

Cites:

Cited by:

Related to: