Abstract Software components, arising, typically, in systems ’ analysis and design, are characterized by a public interface and a private encapsulated state. They persist (and evolve) in time, according to some behavioural patterns. This paper is an exercise in modeling such components as coalgebras for some kinds of endofunctors on ¢¡¤ £ , capturing both (interface) types and behavioural aspects. The construction of component categories, cofibred over the interface space, emerges by generalizing the usual notion of a coalgebra morphism. A collection of composition operators as well as a generic notion of bisimilarity, are discussed.

. This paper accompanies the demonstration of Camila, an experimental platform for formal software development, rooted in the tradition of constructive specification methods. The Camila approach is an attempt to make available at software development level the basic problem solving strategy one got used to from school physics --- create, experiment and reason on a mathematical model. Based on a notion of formal software component, it encompasses a set-theoretic language and an inequational calculus for classification and refinement. Its kernel is a functional prototyping environment, fully connectable to external applications, equipped with a classified component repository and distribution facilities.