From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5948 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Re: The humility topos Date: Fri, 02 Jul 2010 09:02:25 +0100 Message-ID: References: Reply-To: Steve Vickers NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1278261258 21586 80.91.229.12 (4 Jul 2010 16:34:18 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 4 Jul 2010 16:34:18 +0000 (UTC) Cc: Categories list To: Dusko Pavlovic Original-X-From: categories@mta.ca Sun Jul 04 18:34:16 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OVS92-0000uV-MD for gsmc-categories@m.gmane.org; Sun, 04 Jul 2010 18:34:16 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OVRfm-00070u-Pe for categories-list@mta.ca; Sun, 04 Jul 2010 13:04:02 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5948 Archived-At: I've assumed (and told people) that "topos" was a back-formation from "topology" - that Grothendieck's intention was to imply that toposes were the structures of which topology was truly the study. (The argument falls into two parts: (a) to carry out topology you need sheaves and not just opens, and (b) there are suitable categories of sheaves that don't arise from ordinary spaces.) Certainly it is my own intention to stress the "generalized topological space" nature of toposes; but is my assumption about Grothendieck's intention actually correct? Steve. Dusko Pavlovic wrote: > It might be fair to remember that "Topoi" is the title of 6th book or > Aristotle's Organon. "On Categories" is the title of the 1st book of > Organon. > > Both concepts were very actively used by scolastic philosophers. > Maybe we are their heirs of some sort ;) > > It would be interesting to know about the motivations of people who > introduced these terms into mathematics. I think that MacLane said at > one point that there was a terminological link through Rudolf Carnap, > thus through neokantians. The notion of categories plays a prominent > role in Kant's first Critique. But it is even more interesting if the > term topos was introduced with an intentional reference to > *dialectics*, which is what that part of Organon is about. > > -- dusko [For admin and other information see: http://www.mta.ca/~cat-dist/ ]