The coalgebraic view on classes and objects is elaborated to include inheritance. Inheritance in coalgebraic specification (of classes) will be understood dually to parametrization in algebraic specification. That is, inheritance involves restriction (specialization), where parametrization involves extension. And cofree constructions are "best" restrictions, like free constructions are "best" extensions. To make this view on inheritance precise we need a suitable notion of behaviour preserving morphism between classes, which will be defined as a "coalgebra map up-to-bisimulation". AMS Subject Classification (1991): 18C10, 03G30 CR Subject Classification (1991): D.1.5, D.2.1, E.1, F.1.1, F.3.0 Keywords & Phrases: object, class, inheritance, coalgebraic specification, bisimulation 1. Introduction Two basic relations in object-oriented languages are: object o belongs to class C, and: class C inherits from class C 0 (see e.g. [20]). Class membership yields what is sometimes called a...