From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4553 Path: news.gmane.org!not-for-mail From: "Nikita Danilov" Newsgroups: gmane.science.mathematics.categories Subject: Re: Categories and functors, query Date: Tue, 9 Sep 2008 14:53:03 +0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241020022 13820 80.91.229.2 (29 Apr 2009 15:47:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:02 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Sep 9 09:02:02 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 09 Sep 2008 09:02:02 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Kd1q5-0007Wz-O7 for categories-list@mta.ca; Tue, 09 Sep 2008 08:56:57 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 23 Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:4553 Archived-At: Michael Barr writes: > > This reminds me of a speculation I have often had (although Saunders > denied and he knew Birkhoff pretty well). In the 30s and 40s, the word > "homomorphism" was regularly used but always meant surjective. By the > late 40s and 50s people were talking about "homomorphism into" meaning not > necessarily surjective. So groups had lattices of subgroups and lattices > of quotient groups and Birkhoff invented lattice theory at least partly in > the hope that the structure of those two lattices would tell you a lot > about the structure of the group. I don't think this actually happened to > any great extent. But I have wondered whether Birkhoff might instead have Noether's `set theoretic foundations of group theory', where group axioms are based on a notion of coset decomposition rather than multiplication, seems to be much earlier (20s) attempt to the same: http://www.math.jussieu.fr/~leila/grothendieckcircle/mclarty2.pdf > > Michael Nikita.