From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9424 Path: news.gmane.org!.POSTED!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Re: How can we have a categorical definition of "theory" Date: Fri, 10 Nov 2017 17:28:04 +0000 Message-ID: References: <5A05AAB4.5020000@cs.bham.ac.uk> <508ad670e2ff1525f0596b3c79485c04@cs.umu.se> Reply-To: Steve Vickers NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: blaine.gmane.org 1510361622 31994 195.159.176.226 (11 Nov 2017 00:53:42 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sat, 11 Nov 2017 00:53:42 +0000 (UTC) Cc: categories@mta.ca To: peklund@cs.umu.se Original-X-From: majordomo@mlist.mta.ca Sat Nov 11 01:53:38 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 1eDK3C-0007xa-9w for gsmc-categories@m.gmane.org; Sat, 11 Nov 2017 01:53:34 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:59705) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1eDK45-0005lG-V0; Fri, 10 Nov 2017 20:54:29 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1eDK2e-0000f2-SB for categories-list@mlist.mta.ca; Fri, 10 Nov 2017 20:53:00 -0400 In-Reply-To: <508ad670e2ff1525f0596b3c79485c04@cs.umu.se> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9424 Archived-At: Dear Patrik, It's absolutely vital to Grothendieck's idea of toposes as generalized spaces. It's essentially categorical logic that allows you to think of toposes as spaces and geometric morphisms as continuous maps. For an introduction, see my TACL talks http://www.cs.bham.ac.uk/~sjv/talks.php particularly numbers 1-4 (the Olomouc tutorials). Steve. On 10/11/2017 16:49, peklund@cs.umu.se wrote: > ... > > Categorical "logic" in a topos to me makes no practical sense at all. > > Patrik > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]