From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5821 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: "injective" terminology Date: Wed, 19 May 2010 10:27:06 +0100 (BST) Message-ID: References: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1274315050 2938 80.91.229.12 (20 May 2010 00:24:10 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 20 May 2010 00:24:10 +0000 (UTC) To: Michael Barr Original-X-From: categories@mta.ca Thu May 20 02:24:08 2010 connect(): No such file or directory Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OEtYW-0008Tp-9q for gsmc-categories@m.gmane.org; Thu, 20 May 2010 02:24:08 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OEt63-0006zq-KN for categories-list@mta.ca; Wed, 19 May 2010 20:54:43 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5821 Archived-At: Like Michael, I've occasionally been bothered by the conflict between the two uses of "injective". However, for me it's the use of the word as a dual for "projective" that feels wrong; the opposite of "pro" is not "in" but "con" (or "contra"). Also, the use of "injective" and "surjective" for maps is so well established throughout mathematics that I don't think there is any chance of changing it. I've thought of using "coprojective" for the dual of "projective"; but for anyone with a classical education that word means "shit-throwing". Peter Johnstone ---------------------- On Tue, 18 May 2010, Michael Barr wrote: > Since there has been such a lively discussion of language (which I have > kept out of because I have seen too many papers start out by saying, "By > ring, we mean a commutative ring with unit"), I though I would bring up > one that has long bothered me. There are too many contexts in which you > have a concrete category (say of compact hausdorff spaces) in which you > are dealing with both injective objects and 1-1 maps that I feel we need a > better word for the latter than "injective". Of course, I could just > revert to 1-1 and perhaps I will. But we have "projective" and > "surjective" for the dual. This suggests "superjective", except that > that is so ugly. > > Any thoughts? > > Michael > > P.S. I originally used *-autonomous to mean symmetric and then I wrote a > paper called, "Non-symmetric *-autonomous categories", so I am just as > guilty. > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]