Coalgebraic models of Omega-groups

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.