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arXiv · 2510.22653

Coalgebraic models of Omega-groups

Maria Bevilacqua
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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.

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Maria Bevilacqua. 2025-10-26. Coalgebraic models of Omega-groups. https://doi.org/10.1007/s10485-026-09890-y

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