From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2399 Path: news.gmane.org!not-for-mail From: Ronald Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: chain complexes: in reply to John Baez Date: Sun, 20 Jul 2003 17:43:55 +0100 Message-ID: <5.0.2.1.0.20030720173046.00a8aec0@pop.freeserve.com> References: <200307140729.h6E7TUn18042@math-cl-n01.ucr.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Trace: ger.gmane.org 1241018633 3957 80.91.229.2 (29 Apr 2009 15:23:53 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:23:53 +0000 (UTC) To: categories@mta.ca (categories) Original-X-From: rrosebru@mta.ca Mon Jul 21 10:53:56 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 21 Jul 2003 10:53:56 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19eb6n-0006AI-00 for categories-list@mta.ca; Mon, 21 Jul 2003 10:53:45 -0300 X-Sender: ll319dg.fsnet.co.uk@pop.freeserve.com X-Mailer: QUALCOMM Windows Eudora Version 5.0.2 In-Reply-To: <200307140729.h6E7TUn18042@math-cl-n01.ucr.edu> Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 27 Original-Lines: 42 Xref: news.gmane.org gmane.science.mathematics.categories:2399 Archived-At: reply to r.brown@bangor.ac.uk The paper (R. BROWN and HIGGINS, P.J.), `Cubical abelian groups with connections are equivalent to chain complexes', Homology, Homotopy and Applications, 5(1) (2003) 49-52. has a reference to Grothendieck's `cat\'egorie cofibr\'ee....' (1968) SLNM 79, (the canonical reference for the first question), and also to Bourn (JPAA 1990), and gives a proof that 5 different structures are, in an additive category with kernels, equivalent to chain complexes. Among these structures is strict globular omega-categories. However, this is deduced from some non abelian and more difficult results. Ronnie Brown Dear Categorists - Who first showed that an internal category in the category of abelian groups was a 2-term chain complex of abelian groups? What's a good reference? Who first showed that an internal strict omega-category in the category of abelian groups was a chain complex of abelian groups? What's a good reference? (Of course for "internal X in the category of Y's", I am willing to accept "internal Y in the category of X's" as a substitute.) Best, jb