From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2069 Path: news.gmane.org!not-for-mail From: Mark Hovey Newsgroups: gmane.science.mathematics.categories Subject: Enriched locally presentable categories Date: 26 Dec 2001 07:18:19 -0500 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241018381 2288 80.91.229.2 (29 Apr 2009 15:19:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:19:41 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat Dec 29 20:19:27 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 29 Dec 2001 20:19:27 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16KTZe-0008Tm-00 for categories-list@mta.ca; Sat, 29 Dec 2001 20:11:34 -0400 User-Agent: Gnus/5.070095 (Pterodactyl Gnus v0.95) Emacs/20.3 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 46 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:2069 Archived-At: I am still trying to understand some enriched category theory. Suppose V is a closed symmetric monoidal category that is also locally presentable. Suppose C is a small V-category. I am interested in the category of V-functors from C to V, and, in particular, I want to know that it is locally presentable. Might need some hypotheses on C for this, but I would prefer to avoid hypotheses on the actual functors. This time I have actually looked in Kelly's book and I did not see it, but I confess to finding this subject rough going so might have missed it. On the other hand, my library is closed for the holiday, so I have not looked at Adamek and Rosicky's book on enriched category theory yet. I guess the generators ought to be the representable functors. I know everything is a weighted colimit of representables, but I don't know whether this colimit is filtered enough, nor do I know whether one can get away with weighted colimits instead of ordinary ones. One direction this might go is to develop a theory of locally presentable in an enriched sense, using weighted colimits instead of colimits. I would prefer to avoid that if possible. Happy holidays to all. Mark Hovey