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''.

Object-oriented Programming (acm D.1.5), Requirements/Specifications (acm D.2.1), DATA STRUCTURES (acm E.1), Models of Computation (acm F.1.1), General (acm F.3.0)
Theories (e.g. algebraic theories), structure, and semantics (msc 18C10), Categorical logic, topoi (msc 03G30)
Department of Computer Science [CS]

Jacobs, B.P.F. (1995). Inheritance and cofree constructions. Department of Computer Science [CS]. CWI.