The contribution of this paper is twofold: first, it defines a unified framework for modeling abstract components, as well as a formalization of integration rules to combine their behaviour. This is based on a coalgebraic definition of components, which is a categorical representation allowing the unification of a large family of formalisms for specifying state-based systems. Second, it studies compositional conformance testing i.e. checking whether an implementation made of correct interacting components combined with integration operators conforms to its specification.