Equational axiomatizability for coalgebra

Equational axiomatizability for coalgebra

A characterization result for equationally deenable classes of certain coalgebras (including basic hidden algebra) shows that a class of coalgebras is deenable by equations if and only if it is closed under coproducts, quotients, sources of morphisms and representative inclusions. The notions of equation and satisfaction are axiomatized in order to include the diierent approaches in the literat...

Equational Axiomatizability for Coalgebra

A characterization result for equationally de nable classes of certain coalgebras (including basic hidden algebra) shows that a class of coalgebras is de nable by equations if and only if it is closed under coproducts, quotients, sources of morphisms and representative inclusions. The notions of equation and satisfaction are axiomatized in order to include the di erent approaches in the literat...

Axiomatizability in Inclusive Equational Logic

A Birkhoo-like Axiomatizability Result for Hidden Algebra and Coalgebra

A characterization result for behaviorally deenable classes of hidden algebras shows that a class of hidden algebras is behaviorally deenable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically generalizes this result to a framework of any category with coproducts, a nal object and an inclusion...

A Birkhoff-like Axiomatizability Result for Hidden Algebra and Coalgebra

A characterization result for behaviorally de nable classes of hidden algebras shows that a class of hidden algebras is behaviorally de nable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically generalizes this result to a framework of any category with coproducts, a nal object and an inclusion...