Coalgebraic models of Omega-groups
Category Theory
2025-11-12 v2 Logic
Quantum Algebra
Rings and Algebras
Abstract
We investigate models of algebraic theories in the category of cocommutative coalgebras over a field. We establish some of their categorical properties, similar to those of algebraic varieties. We introduce a class of categories of coalgebraic models of algebraic theories endowed with an underlying structure of cocommutative Hopf algebra, and show that these categories are semi-abelian. We call them ``categories of Omega-Hopf algebras'', since it is possible to characterize them as coalgebraic models of algebraic theories of Omega-groups.
Cite
@article{arxiv.2510.22653,
title = {Coalgebraic models of Omega-groups},
author = {Maria Bevilacqua},
journal= {arXiv preprint arXiv:2510.22653},
year = {2025}
}