From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6656 Path: news.gmane.org!not-for-mail From: Charles Wells Newsgroups: gmane.science.mathematics.categories Subject: Re: Explanations Date: Sat, 30 Apr 2011 14:58:14 -0500 Message-ID: References: Reply-To: Charles Wells 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 1304337987 25233 80.91.229.12 (2 May 2011 12:06:27 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 2 May 2011 12:06:27 +0000 (UTC) To: peasthope@shaw.ca, catbb Original-X-From: majordomo@mlist.mta.ca Mon May 02 14:06:20 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QGrtM-0005sP-Hs for gsmc-categories@m.gmane.org; Mon, 02 May 2011 14:06:20 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:39543) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QGrpD-0005Hd-QB; Mon, 02 May 2011 09:02:03 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QGrp9-00044X-Qt for categories-list@mlist.mta.ca; Mon, 02 May 2011 09:02:00 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6656 Archived-At: In the expression "any x:T->X" the T depends on x.=A0 If you use the arrow notation you seem bound to name the domain of the morphism.=A0 You could say "for any x with codomain X there is an e:dom x -> X ..." but in the rest of the sentence you will have to mention the domain again. My impression is that notation "any x:T->X" where T depends on x without that fact being mentioned is common in category theory writing.=A0 There is nothing wrong with this if a reader understands the intent. I would call it "suppression of dependence".=A0 In the Handbook I talked about suppression of parameters, but this is not suppression of parameters.=A0 It is something I had not noticed before. Are there other situations in math where this happens? On Fri, Apr 29, 2011 at 2:56 PM, wrote: > > Charles & everyone, > > Earlier peasthope wrote, > "...changing a few words of a sentence can make a concept obvious rather > than nebulous". =A0Revise that to "obvious rather than difficult". > > From: =A0 Charles Wells > Date: =A0 Fri, 22 Apr 2011 09:37:44 -0500 >> Can you give specific examples? =A0I suspect that in most cases the cha= nge >> introduces a useful metaphor that was hidden before. > > Here is a small example from the _Conceptual Mathematics_ of > Lawvere and Schanuel. =A0No offense to the authors or the book. > It's an indispensible and invaluable resource. > > L&S page 292, "Definition ... equalizer ... and for each x:T-->X ... ther= e is > exactly one e:T-->E ... ." =A0 =A0"For all T" is implicit. > > http://en.wikipedia.org/wiki/Equalizer_(Mathematics) , "In category theor= y > ... defined by a universal property, ... object E and morphism eq ... suc= h that, > given any other object O and morphism m ... ." > > For me, the reference to "any other object O" helps. =A0The definition in= the > Wikipedia seems to reveal the "universality" of the equalizer better. =A0= The > diagram also helps. > > A trivial issue for most readers but a small detail can make a difference= for > a student. > > Regards, =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 ... Peter E. > > -- > Telephone 1 360 450 2132. =A0bcc: peasthope at shaw.ca > Shop pages http://carnot.yi.org/ accessible as long as the old drives sur= vive. > Personal pages http://members.shaw.ca/peasthope/ . > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]