From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6653 Path: news.gmane.org!not-for-mail From: peasthope@shaw.ca Newsgroups: gmane.science.mathematics.categories Subject: Re: Explanations Date: Fri, 29 Apr 2011 11:56:48 -0800 Message-ID: References: Reply-To: peasthope@shaw.ca NNTP-Posting-Host: lo.gmane.org X-Trace: dough.gmane.org 1304191689 21506 80.91.229.12 (30 Apr 2011 19:28:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 30 Apr 2011 19:28:09 +0000 (UTC) Cc: peasthope@shaw.ca To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sat Apr 30 21:28:03 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 1QGFpi-0004dw-H0 for gsmc-categories@m.gmane.org; Sat, 30 Apr 2011 21:28:02 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:41056) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QGFn6-0002pO-70; Sat, 30 Apr 2011 16:25:20 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QGFn2-0006ah-FD for categories-list@mlist.mta.ca; Sat, 30 Apr 2011 16:25:16 -0300 in-reply-to: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6653 Archived-At: Charles & everyone, Earlier peasthope wrote, "...changing a few words of a sentence can make a concept obvious rather 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 change > 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 ... there is exactly one e:T-->E ... ." "For all T" is implicit. http://en.wikipedia.org/wiki/Equalizer_(Mathematics) , "In category theory ... defined by a universal property, ... object E and morphism eq ... such 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 difference 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/ ]