From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6657 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Explanations Date: Sat, 30 Apr 2011 17:09:22 -0400 Message-ID: Reply-To: "Fred E.J. Linton" 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 1304337997 25295 80.91.229.12 (2 May 2011 12:06:37 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 2 May 2011 12:06:37 +0000 (UTC) Cc: "categories" To: Original-X-From: majordomo@mlist.mta.ca Mon May 02 14:06:33 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 1QGrtX-000626-Ff for gsmc-categories@m.gmane.org; Mon, 02 May 2011 14:06:31 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:39549) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QGrps-0005KN-8Q; Mon, 02 May 2011 09:02:44 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QGrpp-00045V-Ik for categories-list@mlist.mta.ca; Mon, 02 May 2011 09:02:41 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6657 Archived-At: Hi, Peter, Actually, the word "other" below introduces a red herring: there is in fact every reason *not* to wish to restrict = attention only to objects O *other* than E or T or X -- indeed, = I can imagine that there might be settings in which there are = *no* objects "other than" E or T or X, in which case the = Wikipedia verbiage quoted paints you into a corner you really = *don't* want to be in :-) . Cheers, -- Fred ------ Original Message ------ Received: Sat, 30 Apr 2011 03:30:49 PM EDT From: peasthope@shaw.ca To: categories@mta.ca Cc: peasthope@shaw.ca Subject: categories: Re: Explanations > Charles & everyone, > = > Earlier peasthope wrote, > "...changing a few words of a sentence can make a concept obvious rathe= r > than nebulous". Revise that to "obvious rather than difficult". > = > From: Charles Wells > Date: Fri, 22 Apr 2011 09:37:44 -0500 >> Can you give specific examples? I 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. No 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 ... th= ere is > exactly one e:T-->E ... ." "For all T" is implicit. > = > http://en.wikipedia.org/wiki/Equalizer_(Mathematics) , "In category the= ory > ... defined by a universal property, ... object E and morphism eq ... s= uch that, > given any other object O and morphism m ... ." > = > For me, the reference to "any other object O" helps. The definition in= the > Wikipedia seems to reveal the "universality" of the equalizer better. = The > diagram also helps. > = > A trivial issue for most readers but a small detail can make a differen= ce for > a student. > = > Regards, ... Peter E. > = > -- = > Telephone 1 360 450 2132. bcc: peasthope at shaw.ca > Shop pages http://carnot.yi.org/ accessible as long as the old drives survive. > Personal pages http://members.shaw.ca/peasthope/ . > = > = > = > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]