From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2070 Path: news.gmane.org!not-for-mail From: maxk@maths.usyd.edu.au (Max Kelly) Newsgroups: gmane.science.mathematics.categories Subject: Re: Enriched locally presentable categories Date: Mon, 31 Dec 2001 19:30:27 +1100 (EST) Message-ID: <200112310830.fBV8URA305918@milan.maths.usyd.edu.au> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018382 2292 80.91.229.2 (29 Apr 2009 15:19:42 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:19:42 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Dec 31 10:55:38 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 31 Dec 2001 10:55:38 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16L3l0-0005n4-00 for categories-list@mta.ca; Mon, 31 Dec 2001 10:49:42 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 47 Original-Lines: 23 Xref: news.gmane.org gmane.science.mathematics.categories:2070 Archived-At: Mark Hovey's letter of 26 Dec - known as Boxing Day in the British-speaking world - suggests that it might be a good idea to develop a theory of local presentability and all that in the context of enriched categories. In fact such a theory was developed in my paper [Structures defined by finite limits in the enriched context I, Cahiers de Top. et Geom. Differentielles 23 (1982), 3 - 42]. Everything works very smoothly; but there are a few annoying misprints, many of which seem to be my own fault. Further developments can be found in [Blackwell-Kelly-Power, Two-dimensional monad theory, J. Pure Appl. Algebra 59 (1989), 1 - 41] and in [Kelly-Power, Adjunctions whose counits are coequalizers and presentations of finitary enriched monads, J. Pure Appl. Algebra 89 (1993), 163 - 179], among other papers of myself and of others; Brian Day, Steve Lack, John Power, and Ross Street have all written on related matters. Please accept, Mark, my best wishes for your future work in this direction. In any case, New Year's Eve is a fine time to send greetings more generally to Bob and all on this Bulletin Board. Warm regards - Max Kelly.