Equational and implicational classes of coalgebras

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 results are analogous to the theorems of Birkho4 and of Mal’cev in classical universal algebra. c � 2001 Elsevier Science B.V. All rights reserved.

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