when i was talking to baez this evening he asked me a question that confused me...

i'm probably jusy making some silly mistake here...

the question is something like... oh, maybe my mistake was sillier than i'd realized...

when you take the free abelian category on an algebroid, first you freely adjoin limits, and then you freely adjoin colimits... and then for some reason you stop there, even though you _could_ go ahead and adjoin some new limits without disturbing the old ones...

but apparently why i was confused is that i forgot that during the stage where you freely adjoin the colimits, the limits that were previously freely adjoined are of course preserved because the yoneda embedding (the free cocompletion...) always preserves all limits...