From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8978 Path: news.gmane.org!.POSTED!not-for-mail From: Tom Avery Newsgroups: gmane.science.mathematics.categories Subject: Product-preserving sub-representables Date: Mon, 10 Oct 2016 16:50:12 +0100 Message-ID: Reply-To: Tom Avery NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-1"; format=flowed Content-Transfer-Encoding: 7bit X-Trace: blaine.gmane.org 1476368440 19860 195.159.176.226 (13 Oct 2016 14:20:40 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Thu, 13 Oct 2016 14:20:40 +0000 (UTC) To: Original-X-From: majordomo@mlist.mta.ca Thu Oct 13 16:20:33 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 1bugs2-0003wa-88 for gsmc-categories@m.gmane.org; Thu, 13 Oct 2016 16:20:30 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:58979) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1bugrL-0007dz-0Y; Thu, 13 Oct 2016 11:19:47 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1bugr8-00069X-0S for categories-list@mlist.mta.ca; Thu, 13 Oct 2016 11:19:34 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8978 Archived-At: Dear categorists, I've recently had reason to consider presheaves P : C^op --> Set on a category C with the following two properties: - P preserves all small products (i.e. sends coproducts in C to products in Set), and - P is a subfunctor of a representable presheaf. Is anyone aware of situations where presheaves with both of these properties are significant? In particular, I'm interested in categories C for which every such P is representable. The only examples I'm aware of are Set, Vect, and any poset with arbitrary joins. Does anyone know of any more? Best wishes, Tom Avery -- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]