Scott domains, originated and commonly used in formal semantics of computer languages, were generalized by J. Adámek to Scott complete categories. We prove that the categorical counterpart of the result of D. Scott – the existence of a countable based Scott domain universal with respect to all countably based Scott domains – is no longer valid for the categorical generalization. However, all obstacles disappear if the notion of the Scott complete category is weakened to a categorical counterpart of bifinite domains.