From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9411 Path: news.gmane.org!.POSTED!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: Some questions about different notions of "theory" Date: Mon, 6 Nov 2017 18:13:11 -0700 Message-ID: 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 1510094951 25768 195.159.176.226 (7 Nov 2017 22:49:11 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 7 Nov 2017 22:49:11 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Tue Nov 07 23:49:06 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 1eCCg5-0006UE-HB for gsmc-categories@m.gmane.org; Tue, 07 Nov 2017 23:49:05 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:58824) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1eCCg3-0002pG-Qq; Tue, 07 Nov 2017 18:49:03 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1eCCec-00004q-Ns for categories-list@mlist.mta.ca; Tue, 07 Nov 2017 18:47:34 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9411 Archived-At: 1) Finitary monads correspond to Lawvere theories. Is there a name for those monads that correspond to toposes? 2) In topos theory is there any analogous result to Lawvere's theorem that the opposite of the category of free finitely generated gadgets is equivalent to the Lawvere theory of gadgets? Something like "the opposite of the category of fooable gadgets is equivalent to the topos of gadgets"? 3) nLab says a sketch is a small category T equipped with subsets (L,C) of its limit cones and colimit cocones. A model of a sketch is a Set-valued functor preserving the specified limits and colimits. Is preserving limits and colimits like a ring homomorphism? Preserving both limits and colimits sounds like it ought to involve profunctors, but maybe I'm level slipping. -- 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/ ]