From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9740 Path: news.gmane.org!.POSTED!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: characterization of flp endofucntors on Set? Date: Wed, 24 Oct 2018 12:56:35 +0200 Message-ID: References: <8C57894C7413F04A98DDF5629FEC90B147A54657@Pli.gst.uqam.ca> Reply-To: Thomas Streicher NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" X-Trace: blaine.gmane.org 1540427024 7011 195.159.176.226 (25 Oct 2018 00:23:44 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Thu, 25 Oct 2018 00:23:44 +0000 (UTC) Cc: Richard Garner , "categories@mta.ca" To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Original-X-From: majordomo@mlist.mta.ca Thu Oct 25 02:23:40 2018 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 1gFTR6-0001iE-5V for gsmc-categories@m.gmane.org; Thu, 25 Oct 2018 02:23:40 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:58250) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1gFTSB-0007pC-G4; Wed, 24 Oct 2018 21:24:47 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1gFTR0-0002QB-7z for categories-list@mlist.mta.ca; Wed, 24 Oct 2018 21:23:34 -0300 Content-Disposition: inline In-Reply-To: <8C57894C7413F04A98DDF5629FEC90B147A54657@Pli.gst.uqam.ca> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9740 Archived-At: Dear Andr'e, I think we can't do better than exhibiting Hom(L,-) as the directed colimit of the Set(X,-) indexed by f : L -> X. > I have a question regarding certain finite limit preserving functors Set-->Set. > > If L is a locale, then the functor Hom(L,-):Set-->Set preserves finite limits, > where Hom(L,X) denotes the set of morphisms of locales L-->X for a discrete locale X. > Is there is a simple characterization of these flp functors? I think I should reveil the background of my question. Look at p.7 of my https://www2.mathematik.tu-darmstadt.de/~streicher/FIBR/UniGround.pdf for formulations of my conditions Tr1-Tr3. I think Hom(L,-) validates (Tr1) and (Tr2) but presumably not (Tr3) (for EE = SS =Set). I am looking for a functor F : Set->Set validating all 3 conditions but not being equivalent to Id_Set. Butmaybe there is none? Best, Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]