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