From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9736 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: Tue, 23 Oct 2018 10:56:25 +0200 Message-ID: References: <1540252918.3297329.1551071616.650AD098@webmail.messagingengine.com> 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 1540308069 27146 195.159.176.226 (23 Oct 2018 15:21:09 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 23 Oct 2018 15:21:09 +0000 (UTC) Cc: To: Richard Garner Original-X-From: majordomo@mlist.mta.ca Tue Oct 23 17:21:05 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 1gEyUR-0006wP-G2 for gsmc-categories@m.gmane.org; Tue, 23 Oct 2018 17:21:03 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:57518) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1gEyWd-0004fP-Fk; Tue, 23 Oct 2018 12:23:19 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1gEyVT-0004AK-BW for categories-list@mlist.mta.ca; Tue, 23 Oct 2018 12:22:07 -0300 Content-Disposition: inline In-Reply-To: <1540252918.3297329.1551071616.650AD098@webmail.messagingengine.com> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9736 Archived-At: Dear Richard, thanks for your answer. Offline I have received a reply by Jonas Frey which answers my question satisfactorily. Let U be a Groth. universe then Lex(U,Set) consists of filtered/directed colimits of representables. Accordingly, Lex(U,U) is equivalent to the full subcat of Set^U on U-small directed colimits of representables. But that sounds related to what Blass says, isn't it. Best, Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]