Suppose that I have a category $C$ which has all finite limits and colimits. I have read that in general the canonical functor $C \to Ind(C)$ does not behave nicely with respect to filtered colimits.
Suppose that $I$ is a filtered category and a $F$ functor from $I$ to $C$. I would like to know that if the colimit (when computed in $C$) exists, it agrees with the colimit (when computed in $Ind(C)$).
Now I understand this to be false in general (this is the not behaving nicely part). However, perhaps under some extra reasonable assumptions on $C$ it is known to be true? For instance, I am willing to assume that $C$ is quasi-abelian and has enough projectives and injectives.