The formal ball model for -categories

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.

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