From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9116 Path: news.gmane.org!.POSTED!not-for-mail From: Jean Benabou Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology Date: Tue, 14 Feb 2017 10:39:20 +0100 Message-ID: References: <070VBkupz0000S02.1486845771@web02.cms.usa.net> <02568D97-0A72-4CA8-8900-BDE11E890890@cs.bham.ac.uk> Reply-To: Jean Benabou NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=ISO-8859-1; format=flowed; delsp=yes Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1487084096 7982 195.159.176.226 (14 Feb 2017 14:54:56 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 14 Feb 2017 14:54:56 +0000 (UTC) Cc: "Fred E.J. Linton" , Categories To: Steve Vickers Original-X-From: majordomo@mlist.mta.ca Tue Feb 14 15:54:50 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1cdeVF-0001ey-HG for gsmc-categories@m.gmane.org; Tue, 14 Feb 2017 15:54:49 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:43512) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cdeUg-0005g0-PM; Tue, 14 Feb 2017 10:54:14 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cdeU9-0007vj-MZ for categories-list@mlist.mta.ca; Tue, 14 Feb 2017 10:53:41 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9116 Archived-At: Dear Steve, I totally agree with you. Let me apply your zoological criteria to Category Theory. You begin =20 with the very simple notions of category, functor and natural =20 transformation. But then you start piling in subclauses such as =20 categories with finite limits, or regular, or abelian, or the glorious =20= toposes. For functors you refine the notion to fully faithful ones or =20= those who have an adjoint, or are flat, or are fibrations. I could =20 give hundreds of examples, and even a meticulous zoologist would =20 say:To much is to much! Obviously Category Theory is very bad and the very idea of putting in =20= a same bag groups, topological spaces, locales, and the glorious =20 toposes is a misconception. Serious mathematicians agreed with this. You are too young to remember =20= the time when these mathematicians called, with zoological =20 justification, this theory : Abstract general nonsense. All the best, Jean Le 14 f=E9vr. 17 =E0 09:48, Steve Vickers a =E9crit : > Dear Fred, > > A good answer, but my point was that it was a bad question. > > You see this once you start pressing at the details. Are seals and =20 > turtles fish? No, but on your definition it depends on whether =20 > flippers count as legs or not. What about sea snakes? Obviously not =20= > - they're snakes, that just happen to live in the sea. But then eels =20= > do seem a bit more fishy. > > A meticulous zoologist would start piling on the subclauses to pin =20 > it down more precisely, but we know that that does not actually =20 > refine our understanding of zoology. It just amplifies the =20 > misconceptions underlying the original question. > > I'm saying the same can happen in mathematics. > > All the best, > > Steve. > >> On 11 Feb 2017, at 20:42, Fred E.J. Linton wrote: >> >> Steve, et al., >> >> If you want >> >>> a definition of "fish", but on the understanding that it has to =20 >>> include >> whales >> >> let me offer: "legless marine vertebrates" :-) . >> >> Cheers, -- tlvp >> > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]