From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4056 Path: news.gmane.org!not-for-mail From: Jiri Adamek Newsgroups: gmane.science.mathematics.categories Subject: Functor derivatives - a question and a result Date: Fri, 2 Nov 2007 12:44:10 +0100 (CET) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241019692 11513 80.91.229.2 (29 Apr 2009 15:41:32 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:41:32 +0000 (UTC) To: categories net Original-X-From: rrosebru@mta.ca Fri Nov 2 16:23:46 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 02 Nov 2007 16:23:46 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Io202-0002tG-Vf for categories-list@mta.ca; Fri, 02 Nov 2007 16:16:11 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 8 Original-Lines: 17 Xref: news.gmane.org gmane.science.mathematics.categories:4056 Archived-At: Andre Joyal defined derivatives of analytic functors in his 1986 paper. Recently I heard the more general definition of a derivative F' of an endofunctor F defined via a universal sub-cartesian transformation from F'xId into F. Who is the author of this definition? The following result seems to indicate that outside of the realm of analytic functors derivatives may not be really useful: Theorem. Every non-faithful functor F:Set -> Set has the derivative F' = 0 (the constant functor to the empty set). xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx