From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6954 Path: news.gmane.org!not-for-mail From: Colin McLarty Newsgroups: gmane.science.mathematics.categories Subject: The Maranda-Verdier lemma? Date: Thu, 6 Oct 2011 15:14:59 -0400 Message-ID: Reply-To: Colin McLarty NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1317990829 30044 80.91.229.12 (7 Oct 2011 12:33:49 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 7 Oct 2011 12:33:49 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Fri Oct 07 14:33:41 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1RC9cT-00009y-4H for gsmc-categories@m.gmane.org; Fri, 07 Oct 2011 14:33:41 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:40120) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1RC9aj-0008F3-Vm; Fri, 07 Oct 2011 09:31:53 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RC9ai-0003RE-1R for categories-list@mlist.mta.ca; Fri, 07 Oct 2011 09:31:52 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6954 Archived-At: Many theorems on injectives reduce to the plain case of divisible Abelian groups by the lemma that any functor A-->B with left exact left adjoint and monic unit preserves injectives, and if A has enough injectives so does B. It is a fantastic caseof waht Peter Freyd has said: caegory theory makes what should be trivial actually trivial. The reasoning occurs in Eckmann-Schopf in 1953 but in a special case. It was first published in the Trans. AMS in 1964 by Maranda, and by Verdier the same year in mimeographed notes of SGA 4. I refer to this lemma a lot lately, and I'd like a name for it. So I'm asking here what people think of calling it Maranda-Verdier? best, Colin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]