The representability conjecture for higher-categorical functors

Suppose $A$ is an $n+1$-category admitting arbitrary direct and inverse limits. A functor $h:A^o\rightarrow nCAT'$ is called representable when it is induced by an object of $A$, and a functor $g:A\rightarrow nCAT'$ is representable when it is induced by an object of $A^o$. Representability conjecture. The functor $h$ is representable if and only if it transforms direct limits into inverse limits, while $g$ is representable if and only if it transforms inverse limits into inverse limits. This criterion is used in the paper to obtain internal $\underline{Hom}$ objects, but is not proved there.