From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4070 Path: news.gmane.org!not-for-mail From: Marcelo Fiore Newsgroups: gmane.science.mathematics.categories Subject: Re: Functor derivatives - a question and a result Date: Tue, 6 Nov 2007 11:38:26 +0000 (GMT) Message-ID: References: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241019700 11564 80.91.229.2 (29 Apr 2009 15:41:40 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:41:40 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Nov 6 15:45:05 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 06 Nov 2007 15:45:05 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IpU9R-0005jA-Mm for categories-list@mta.ca; Tue, 06 Nov 2007 15:31:53 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 22 Original-Lines: 35 Xref: news.gmane.org gmane.science.mathematics.categories:4070 Archived-At: On a related matter to the message below by Jiri, let me point out the following paper: M. Fiore. Differential structure in models of multiplicative biadditive intuitionistic linear logic. In Typed Lambda Calculi and Applications (TLCA 2007), LNCS 4583, pp. 163-177, 2007. [Available from ] presenting a categorical framework for differentiation, directly synthetised from the differential calculus of generalised species of structures. Though, as it transpired in conversation with Anders Kock, the setting is also applicable to convenient vector spaces and some models of SDG. On Fri, 2 Nov 2007, Jiri Adamek wrote: > > 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 >