From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9417 Path: news.gmane.org!.POSTED!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: Re: Some questions about different notions of "theory" Date: Thu, 9 Nov 2017 09:03:04 -0700 Message-ID: References: Reply-To: Mike Stay NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" X-Trace: blaine.gmane.org 1510260246 31508 195.159.176.226 (9 Nov 2017 20:44:06 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Thu, 9 Nov 2017 20:44:06 +0000 (UTC) Cc: categories To: ptj@maths.cam.ac.uk Original-X-From: majordomo@mlist.mta.ca Thu Nov 09 21:44:01 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 1eCtg7-0007s1-4y for gsmc-categories@m.gmane.org; Thu, 09 Nov 2017 21:43:59 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:59379) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1eCtgw-0007NI-9J; Thu, 09 Nov 2017 16:44:50 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1eCtfV-0002Zk-Dg for categories-list@mlist.mta.ca; Thu, 09 Nov 2017 16:43:21 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9417 Archived-At: On Tue, Nov 7, 2017 at 4:57 PM, wrote: > 1) I'm not sure what Mike means by `those monads that correspond to toposes' > since most toposes don't correspond to monads on anything. I'm sorry, I meant "those monads that correspond to higher-order theories", where a higher-order theory gets interpreted in a topos in the same way that a Lawvere theory gets interpreted in a category with finite products. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]