categories: limits in Gray-categories

[Steve Lack <stevel@maths.usyd.edu.au>]

Michael Batanin writes (in response to David Carlton):
 > 
 > But now I understand you are asking about weak (or pseudo) colimits. They
 > exist in 1-Cat and 2-Cat and can be expressed in terms of appropriate
 > weighted colimits. I never saw a paper about pseudocolimits in 3-Cat (here
 > we can use Gray-categories instead of general tricatgories). They must be
 > expressed as weighted colimits as well, or a codescent object of a
 > simplicial Gray-category. I'd like to have a reference if such a paper
 > already exists.

Some specific examples of weighted limits in the context of Gray-categories
are considered in:

    Stephen Lack, A coherent approach to pseudomonads, 
    Adv. Math. 152:179-202, 2000.

In particular, I show that the (suitably pseudo) Eilenberg-Moore
object of a pseudomonad can be computed as a weighted limit.
But I don't develop the general theory of pseudocolimits in 3-Cat.


Steve Lack.