From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6659 Path: news.gmane.org!not-for-mail From: "F. William Lawvere" Newsgroups: gmane.science.mathematics.categories Subject: Re: Explanations Date: Sun, 1 May 2011 08:50:18 -0400 Message-ID: References: Reply-To: "F. William Lawvere" 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 1304338133 26237 80.91.229.12 (2 May 2011 12:08:53 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 2 May 2011 12:08:53 +0000 (UTC) To: , Original-X-From: majordomo@mlist.mta.ca Mon May 02 14:08:49 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 1QGrvk-0007JM-6l for gsmc-categories@m.gmane.org; Mon, 02 May 2011 14:08:48 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:52744) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QGrs6-0005WE-Vh; Mon, 02 May 2011 09:05:02 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QGrs0-00046v-LW for categories-list@mlist.mta.ca; Mon, 02 May 2011 09:04:56 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6659 Archived-At: Dear Peter We thought of "other" of course. But that word has no agreed on mathematical definition. Students who think it means "distinct" will be confused when told that it is a special application of the UMP that yields the graph of a map as a section of a projection. (Perhaps best if "self" is a special case of "other" ?) Sammy always scolded Jon=2C Fred=2C Myles=2C and me that such "helpful" explanations make difficult the digestion and mathematical use of simple clear definitions. (I don't think this excludes explanation in a separate paragraph or footnote). Bill > From: peasthope@shaw.ca > Date: Fri=2C 29 Apr 2011 11:56:48 -0800 > To: categories@mta.ca > CC: peasthope@shaw.ca > Subject: categories: Re: Explanations >=20 > Charles & everyone=2C >=20 > Earlier peasthope wrote=2C > "...changing a few words of a sentence can make a concept obvious rather > than nebulous". Revise that to "obvious rather than difficult". >=20 > From: Charles Wells > Date: Fri=2C 22 Apr 2011 09:37:44 -0500 >> Can you give specific examples? I suspect that in most cases the chang= e >> introduces a useful metaphor that was hidden before. >=20 > 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. >=20 > L&S page 292=2C "Definition ... equalizer ... and for each x:T-->X ... th= ere is > exactly one e:T-->E ... ." "For all T" is implicit. >=20 > http://en.wikipedia.org/wiki/Equalizer_(Mathematics) =2C "In category the= ory > ... defined by a universal property=2C ... object E and morphism eq ... s= uch that=2C > given any other object O and morphism m ... ." >=20 > For me=2C the reference to "any other object O" helps. The definition in= the > Wikipedia seems to reveal the "universality" of the equalizer better. Th= e > diagram also helps. >=20 > A trivial issue for most readers but a small detail can make a difference= for > a student. >=20 > Regards=2C ... Peter E. >=20 > --=20 > Telephone 1 360 450 2132. bcc: 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/ . >=20 >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]