It is well known that if \e is a topos, \rar{Colim}{{\ee}^C}{\ee}
\pfl if and only if \m{C} is a filtered internal \cat\.
\par The main result of this paper is that for \e belonging to a wider
class of \cats than topoi, \rar{Colim}{{\ee}^C}{\ee} \pfl if \m{C}
is smooth, proper, and a \uefic\.
\par This result is simplified for topological \cats \e over \m{Set}
that satisfy certain conditions. It is shown that for these \cats
\rar{Colim}{{\ee}^C}{\ee} \pfl if \m{C} is filtered and \m{d_{0C}}
is initial.