From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4954 Path: news.gmane.org!not-for-mail From: Miles Gould Newsgroups: gmane.science.mathematics.categories Subject: Re: Fundamental Theorem of Category Theory? Date: Mon, 8 Jun 2009 21:33:28 +0100 Message-ID: Reply-To: Miles Gould NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1244547609 1615 80.91.229.12 (9 Jun 2009 11:40:09 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 9 Jun 2009 11:40:09 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Tue Jun 09 13:40:06 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MDzgR-000057-N0 for gsmc-categories@m.gmane.org; Tue, 09 Jun 2009 13:40:03 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MDywn-0000jB-16 for categories-list@mta.ca; Tue, 09 Jun 2009 07:52:53 -0300 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4954 Archived-At: On Mon, Jun 08, 2009 at 07:44:40AM -0400, tholen@mathstat.yorku.ca wrote: > You could make your choice more comprehensive: Freyd's General and > Special Adjoint Functor Theorems give a more complete picture of the > fundamental relationship between limit preservation and adjointness. Indeed. I think there's an analogy to be made between these theorems and the Fundamental Theorem of Calculus: one side is very simply stated, and the other requires more care. Compare * d/dx (integral f(x) dx) = f(x), * integral (d/dx f(x)) dx = f(x) [up to constant offset...] with * all right adjoints preserve limits, * all limit-preserving functors [satisfying some caveats...] are right adjoints. Miles [For admin and other information see: http://www.mta.ca/~cat-dist/ ]