From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6084 Path: news.gmane.org!not-for-mail From: Urs Schreiber Newsgroups: gmane.science.mathematics.categories Subject: Re: additive 2-categories and related structures? Date: Tue, 31 Aug 2010 09:47:20 +0200 Message-ID: References: Reply-To: Urs Schreiber NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1283299585 7840 80.91.229.12 (1 Sep 2010 00:06:25 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 1 Sep 2010 00:06:25 +0000 (UTC) Cc: "categories@mta.ca" To: David Roberts ,Ronnie Brown Original-X-From: majordomo@mlist.mta.ca Wed Sep 01 02:06:23 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OqaqM-000818-Sh for gsmc-categories@m.gmane.org; Wed, 01 Sep 2010 02:06:23 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:52755) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OqapK-0003JE-7B; Tue, 31 Aug 2010 21:05:18 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OqapD-0004sX-Sv for categories-list@mlist.mta.ca; Tue, 31 Aug 2010 21:05:12 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6084 Archived-At: Dear Ronnie, only just saw your message via David's reply. Just for completeness it seems one should say that there is quite a bit known about additive n-categories even for n all the way from 1 to infinity -- they are called stable infinity-categories. Examples of these are in particular given by modules over infinity-rings -- which are maybe better known as ring spectra! A modern entry point into the theory, from a category-theoretic point of vi= ew is Jacob Lurie Commutative algebra http://arxiv.org/abs/math/0703204 But the basic elements and examples of the theory, such as E-infinity-rings, A-infinity-algebras and their modules and module categories are of course way older and quite classical even. All the best Urs On Mon, Aug 30, 2010 at 3:18 AM, David Roberts wrote: > Hi Ronnie, > > There is the work of Matthieu Dupont, see his page > > http://breckes.org/dom-en.html > > His PhD thesis is on abelian categories in dimension 2. > > David > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]