From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8998 Path: news.gmane.org!.POSTED!not-for-mail From: Marta Bunge Newsgroups: gmane.science.mathematics.categories Subject: Re: Grothendieck toposes Date: Tue, 1 Nov 2016 15:33:22 +0000 Message-ID: References: ,<30618_1477941855_58179A5F_30618_291_1_E1c1IA3-0007Te-Te@mlist.mta.ca>, Reply-To: Marta Bunge NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1478045454 14197 195.159.176.226 (2 Nov 2016 00:10:54 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Wed, 2 Nov 2016 00:10:54 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Wed Nov 02 01:10:49 2016 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.28]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1c1j8Z-0001w7-M8 for gsmc-categories@m.gmane.org; Wed, 02 Nov 2016 01:10:39 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:60429) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1c1j8B-00079B-Is; Tue, 01 Nov 2016 21:10:15 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1c1j8D-0004XA-Fm for categories-list@mlist.mta.ca; Tue, 01 Nov 2016 21:10:17 -0300 In-Reply-To: Accept-Language: en-CA, en-US Content-Language: en-CA Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8998 Archived-At: Dear Steve, Clemens and Andre, Grothendieck did not come up with the notion of an elementary topos - Lawve= re and Tierney did, so much so that he informally referred to the subobject= s classifier as "the Lawvere object", as Clemens observes. Nevertheless, an= d referring to a remark by Steve, the basic idea of Grothendieck of a categ= ory of sheaves on a site is indeed captured by the more general (and certai= nly less controversial) notion of an S-bounded elementary topos, where S is= an arbitrary elementary topos with an NNO. As for the word "topos", I believe that, in view of its many uses and regar= dless of the meaning "space", it ought to be specified in any context where= one uses it. I find this way of proceeding preferable to identifying it w= ith "Grothendieck topos" as Andre suggests. In addition, I see no reason to= use "logical" instead of "elementary" since the latter is already in use a= nd means "first-order". Best regards, Marta ************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill University Montreal, QC, Canada H3A 2K6 Home: (514) 935-3618 marta.bunge@mcgill.ca http://www.math.mcgill.ca/people/bunge ************************************************ ________________________________ From: Marta Bunge Sent: October 31, 2016 6:40:16 PM To: Steve Vickers Cc: categories@mta.ca Subject: Re: categories: Re: Grothendieck toposes Dear Steve, Thank you for your interesting comments. Grothendieck did not come up with = the notion of an elementary topos - Lawvere and Tierney did, so much so tha= t he informally referred to the subobjects classifier as "the Lawvere objec= t". Nevertheless, the basic idea of Grothendieck of a category of sheaves o= n a site is indeed captured by the more general (and certainly less controv= ersial) notion of an S-bounded elementary topos, where S is an arbitrary el= ementary topos with an NNO. I think that this is what you had in mind. As f= or the word "topos", I believe that it ought to be specified in any context= where one uses it. I find this way of proceeding preferable to identifyin= g it with "Grothendieck topos" as Joyal suggests. Best regards, Marta ************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill University Montreal, QC, Canada H3A 2K6 Home: (514) 935-3618 marta.bunge@mcgill.ca http://www.math.mcgill.ca/people/bunge ************************************************ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]