Equational and implicational classes of coalgebras

Equational and implicational classes of co-algebras

If F : Set → Set is a functor which is bounded and preserves weak generalized pullbacks then a class of F-coalgebras is a covariety, i.e., closed under H (homomorphic images), S (sub-coalgebras) and ∑ (sums), if and only if it can be de0ned by a set of “coequations”. Similarly, quasi-covarieties, i.e., classes closed under H and ∑ , can be characterized by implications of coequations. These res...

Equational Logic of Polynomial Coalgebras

Equational Logi of Polynomial Coalgebras

FUZZY EQUATIONAL CLASSES ARE FUZZY VARIETIES

In the framework of fuzzy algebras with fuzzy equalities and acomplete lattice as a structure of membership values, we investigate fuzzyequational classes. They consist of special fuzzy algebras fullling the samefuzzy identities, dened with respect to fuzzy equalities. We introduce basicnotions and the corresponding operators of universal algebra: construction offuzzy subalgebras, homomorphisms...

Decidable Equational Classes

I will discuss the progress that has been made on solving two open problems dealing with the decidability of the first order theory of equationally defined classes of algebras (varieties).