Re: Inferring colimits

["Dr. P.T. Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>]

> Now for the question.  Has there been any systematic study of what
> I have just defined as repletions?  If not, are there in any case some papers
> I should consider?

I think the question as posed by David (relative to a particular category,
in which some but not all diagrams of a particular shape may have colimits)
is a very hard one. A lot is known about inferring the existence of
particular types of colimits, in arbitrary categories, from the existence
of other types: see the paper by Albert and Kelly "The closure of a class
of colimits" in JPAA 51 (1988), and subsequent references of which Max will
no doubt remind us. But when you work in a particular category, there are
so many ways of "mutilating" the category by omitting particular objects
which are required as the vertices of colimit cones, that I suspect there
is almost nothing you can say in general.

Incidentally, a similar comment applies to David's paper "Multilinearity
of sketches" in TAC 3 (1997): I tried to make this point in my review
(MR 98j:18006).

Peter Johnstone