From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6130 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Re: Grothendieck: more complete URL Date: Thu, 09 Sep 2010 11:43:22 +0100 Message-ID: References: Reply-To: Steve Vickers NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1284075631 23759 80.91.229.12 (9 Sep 2010 23:40:31 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 9 Sep 2010 23:40:31 +0000 (UTC) Cc: Categories list To: Colin McLarty Original-X-From: majordomo@mlist.mta.ca Fri Sep 10 01:40:29 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 1OtqjF-0007Vi-PZ for gsmc-categories@m.gmane.org; Fri, 10 Sep 2010 01:40:29 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50247) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Otqi2-0002jV-Rk; Thu, 09 Sep 2010 20:39:14 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Otqhv-0005Iv-0o for categories-list@mlist.mta.ca; Thu, 09 Sep 2010 20:39:07 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6130 Archived-At: Dear Colin, Can I ask a technical question about foundations here? Does the "enough injectives" result assume a classical base theory? The classical result for module categories uses choice, and my understanding is that the result for sheaf categories uses Barr covers to make available the classical result. I wonder if there's an unequivocally constructive formulation. Regards, Steve. Colin McLarty wrote: > AG intended this paper to hit the very center of homological algebra: > from now on homological algebra is about derived functors on Abelian > categories with enough injectives -- and he justifies this by proving > (against the general expectation) that all sheaf categories have > enough injectives . Of course there are other resolutions besides > injective, we will use them too, but they are special cases for > special purposes. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]