Re: categories: Weighted limits

[Max Kelly <maxk@maths.usyd.edu.au>]

In his letter below, Mark Harvey asks about the functoriality of the
weighted colimit F*G where 
we are dealing with V-categories and say F: K --> V
and G: K --> A.

The matter is dealt with at length in my book ["Basic Concepts of
Enriched Category Theory", London Math Soc. Lecture Notes Series 64,
Cambridge University Press, 1982.]. (The book uses the older terminology
"indexed limit" for "weighted limit" and so on. See Chapter 3, and the
work in Chapter 4 on final and initial weights.

Max Kelly. 
_______________
Subject: 
         categories: Weighted limits
   Date: 
         05 Nov 2001 13:23:24 -0500
  From: 
         Mark Hovey <hovey@picard.math.wesleyan.edu>
     To: 
         categories@mta.ca

Mark Hovey wrote:
> 
> What are the standard references for weighted limits and colimits in
> enriched categories?  I know about Borceux, volume 2, chapter 6, but
> that does not go far enough.
> 
> More precisely, I want to know how functorial the weighted colimit is in
> the weight.  Given a V-natural transformation F --> F', presumably I get
> some kind of map from colim_F G to colim_F' G (or the other way
> around).  I would like a reference for this fact and related functoriality
> facts.
> 
> Presumably the weighted colimit is a bifunctor in the weight and the
> functor one is taking the colimit of, and presumably this bifunctor has
> various good properties.  Has anybody ever written these down?
> 
> Thanks in advance for any help you can give me.
>               Mark Hovey