The fully faithful Yoneda conjecture for higher categories

Suppose $A$ is an $n+1$-category. Its arrow family gives functors

$$\alpha: A \rightarrow \underline{Hom}(A^o, nCAT'),$$ $$\beta: A^o \rightarrow \underline{Hom}(A, nCAT').$$

Yoneda conjecture. The functors $\alpha$ and $\beta$ are fully faithful. This is the higher-categorical analogue of the corresponding fact for $n=0$; the paper gives no proof or resolution.