Yoneda Completion via a DCPO Completion of its Poset of Formal Balls

In this paper, we demonstrate how an idempotent Yoneda completion of quasi-metric spaces can be obtained using the Kostanek-Waszkiewicz Theorem and the dcpo completion of their posets of formal balls. This fills a gap in the current literature concerning the lack of an idempotent Yoneda completion.