Equational axiomatizability for coalgebra

A characterization result for equationally definable classes of certain coa lgebras (including basic hidden algebra) shows that a class of coalgebras i s definable by equations if and only if it is closed under coproducts, quot ients, sources of morphisms and representative inclusions. The notions of e quation and satisfaction are axiomatized in order to include the different approaches in the literature. (C) 2001 Elsevier Science B.V. All rights res erved.