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We investigate under which condition the $\kappa$-ind completion of a functorcategory $C^I$ is equivalent to the category of functors from $I$ to the$\kappa$-ind completion of $C$. A published theorem implies this is true forany Cauchy complete category $C$ and $\kappa$-small category $I$, but we showthis is not the case in general. We prove two results that seem to cover allapplications of this incorrect theorem we could find in the literature: Theresult holds if $C$ has $\kappa$-small colimits and $I$ is $\kappa$-small, orif $C$ is an arbitrary category and $I$ is well-founded and $\kappa$-small. Inboth cases, we show that the conditions are optimal in the sense that theresult holds for all $C$ if and only if $I$ satisfies the given assumption.

When does $\operatorname{Ind}_\kappa(C^I) \simeq \operatorname{Ind}_\kappa(C)^I$?