From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9295 Path: news.gmane.org!.POSTED!not-for-mail From: Robin Cockett Newsgroups: gmane.science.mathematics.categories Subject: Re: An elementary question Date: Mon, 14 Aug 2017 18:51:22 +0000 Message-ID: References: Reply-To: Robin Cockett 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 1502818504 22128 195.159.176.226 (15 Aug 2017 17:35:04 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 15 Aug 2017 17:35:04 +0000 (UTC) To: "categories@mta.ca" , Dana Scott Original-X-From: majordomo@mlist.mta.ca Tue Aug 15 19:34:59 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 1dhfjz-0005Gg-2S for gsmc-categories@m.gmane.org; Tue, 15 Aug 2017 19:34:55 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:43991) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dhfjt-000215-RM; Tue, 15 Aug 2017 14:34:49 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dhfjY-0001hJ-DR for categories-list@mlist.mta.ca; Tue, 15 Aug 2017 14:34:28 -0300 Thread-Topic: categories: An elementary question Thread-Index: AQHTFI2i5vGOx1+5I0KCUyCtg+2D8qKEMd12 In-Reply-To: Accept-Language: en-US Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9295 Archived-At: A great question ... and I do not have an answer for it. However, regard= ing P (<) Q as a (posetal) module between the posets it does have the strik= ing property that it is the final module! -robin ________________________________ From: Dana Scott Sent: Sunday, August 13, 2017 1:55:11 PM To: categories@mta.ca Subject: categories: An elementary question The category of posets (=3D partially ordered sets) and monotone maps is often used as an easy example -- different from the category of sets -- that has products, coproducts, and is cartesian closed but not a topos. Let P and Q be two posets. Define (P (<) Q) as the modified coproduct where all the elements of P are made less than all the elements of Q. QUESTION. Does (P (<) Q) have a nice categorical definition as a functor in the category of posets? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]