From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7734 Path: news.gmane.org!not-for-mail From: Staffan Angere Newsgroups: gmane.science.mathematics.categories,gmane.spam.detected Subject: Isbell & MacLane on the insufficiency on skeletal categories Date: Fri, 24 May 2013 22:34:47 +0000 Message-ID: Reply-To: Staffan Angere NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1369494771 31752 80.91.229.3 (25 May 2013 15:12:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 25 May 2013 15:12:51 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Sat May 25 17:12:52 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1UgG9M-0003mF-CC for gsmc-categories@m.gmane.org; Sat, 25 May 2013 17:12:52 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:60332) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1UgG78-0003in-22; Sat, 25 May 2013 12:10:34 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1UgG77-0001oH-8z for categories-list@mlist.mta.ca; Sat, 25 May 2013 12:10:33 -0300 Precedence: bulk X-Spam-Report: 6.1 points; * 1.8 DATE_IN_PAST_12_24 Date: is 12 to 24 hours before Received: date * 2.5 LOCALPART_IN_SUBJECT Local part of To: address appears in Subject * 1.8 MIME_QP_LONG_LINE RAW: Quoted-printable line longer than 76 chars Xref: news.gmane.org gmane.science.mathematics.categories:7734 gmane.spam.detected:5060098 Archived-At: Dear Category theorists, in Categories for the Working Mathematician, page 164, MacLane relates an a= rgument, "due to Isbell", why one cannot identify all isomorphic objects. I= have not, however, been able to find any publication of Isbell that contai= ns the argument. Does anyone here know if he published it? I also have a question about the argument itself: why is it made the way Ma= cLane does it, rather than just though noticing that all functions from cou= ntable sets are countable, and thus themselves countable, and so isomorphic= to any other countable set? It seems like it would follow directly from th= is that any functions on the natural numbers have to be equal, if isomorphi= c (i.e. equinumerious) sets are identical. Why is MacLane doing all the "de= tours" though products, epics, etc.? Thanks in advance, Staffan= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]