Abstract

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 de ned by a set of “coequations”. Similarly, quasi-covarieties, i.e., classes closed under H and � , can be characterized by implications of coequations. These results are analogous to the theorems of Birkho and of Mal’cev

Citations