We generalise the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann in order to obtain computational models for separated -categories. We fully describe -categories that are
- (a)Yoneda complete
- (b)continuous Yoneda complete
via their formal ball models. Our results yield solutions to two open problems in the theory of quasi-metric spaces by showing that:
- (a)a quasi-metric space X is Yoneda complete if and only if its formal ball model is a dcpo, and
- (b)a quasi-metric space X is continuous and Yoneda complete if and only if its formal ball model BX is a domain that admits a simple characterisation of approximation.