From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1967 Path: news.gmane.org!not-for-mail From: Charles Wells Newsgroups: gmane.science.mathematics.categories Subject: Re: Structure Preserving: Definition? Date: Fri, 18 May 2001 08:49:36 -0400 Message-ID: <4.1.20010518084716.009fb410@mail.oberlin.net> References: <006501c0df13$fe6fb400$87657bc8@athlon> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" X-Trace: ger.gmane.org 1241018237 1436 80.91.229.2 (29 Apr 2009 15:17:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:17:17 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat May 19 00:51:41 2001 -0300 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4J3NBG21106 for categories-list; Sat, 19 May 2001 00:23:11 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: cwells@mail.oberlin.net X-Mailer: QUALCOMM Windows Eudora Pro Version 4.1 In-Reply-To: <006501c0df13$fe6fb400$87657bc8@athlon> Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 35 Original-Lines: 65 Xref: news.gmane.org gmane.science.mathematics.categories:1967 Archived-At: The function # should not have been referred to as a morphism. It is an operation. Operations must be preserved by morphisms, but operations need not be morphisms themselves. (In fact a distributive law is a statement that some operation is a morphism with respect to another operation.) -Charles Wells >Hello, >I've sent the following message to sci.math, but haven't >received a clear answer. I've also tried sci.math.research, >but the moderator bounced the posting. Possibly someone >here can help? > >Derek. >=============================================== > >I'm working through the following paper, trying to learn a bit >more about category theory: > >Matrices, Monads and the Fast Fourier Transform >http://citeseer.nj.nec.com/jay93matrice.html > >I this paper, the author explains vectors in categorical >notation: > >"Vectors are distinguished from lists because their length >is given as part of their structure, represented by a morphism >(function) #: VA -> N." > >What this means is that the morphism '#' will produce the >length of vector. > >However, does this violate one of the requirements that a >morphism must preserve the structure of an object? A vector >is a sequence of elements, and an integer is only a single >value. Does this mean that an integer has the same structure >as a vector? > >Or does "structure preserving morphism" mean something >different? > >Thanks, > >Derek. > > > > > > Charles Wells, Emeritus Professor of Mathematics, Case Western Reserve University Affiliate Scholar, Oberlin College Send all mail to: 105 South Cedar St., Oberlin, Ohio 44074, USA. email: charles@freude.com. home phone: 440 774 1926. professional website: http://www.cwru.edu/artsci/math/wells/home.html personal website: http://www.oberlin.net/~cwells/index.html NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm