TITLE: Does the extension to the pro-completion of a left exact (finite) colimit preserving functor preserve (finite) colimits
QUESTION [6 upvotes]: Let $\mathbf C$ be a category with finite limits.  Then a left exact functor $F\colon \mathbf C\to \mathbf{Set}$ is pro-representable and hence extends to the pro-completion $\mathbf C$.  My question is whether it is true that the extension of $F$ preserves finite colimits whenever $F$ does, and if so what is a reference?  I'm also curious about arbitrary colimits but for the application I care about, finite colimits (or even coequalizers) are enough.

REPLY [2 votes]: I am not certain if he provides the answer to your question, but Dan Isaksen's paper:
Calculating limits and colimits in pro-categories, Fundamenta Mathematicae 175 (2002) 175--194. 
is relevant I think. The point is that the reindexing lemmas in procategories provide a powerful tool for calculating limits and colimits.