From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7717 Path: news.gmane.org!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: (In)accessible comonads and (non)Grothendieck toposes Date: Thu, 9 May 2013 03:07:21 +0000 Message-ID: Reply-To: David Roberts NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1368235328 22910 80.91.229.3 (11 May 2013 01:22:08 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 11 May 2013 01:22:08 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Sat May 11 03:22:08 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1UayVj-0006JE-St for gsmc-categories@m.gmane.org; Sat, 11 May 2013 03:22:08 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:48166) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1UayTZ-0005b5-GI; Fri, 10 May 2013 22:19:53 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1UayTa-0007AW-JX for categories-list@mlist.mta.ca; Fri, 10 May 2013 22:19:54 -0300 Thread-Topic: (In)accessible comonads and (non)Grothendieck toposes Accept-Language: en-AU, en-US Content-Language: en-US Content-ID: <7661639A2DC2A04189FCDE552C1475A5@adelaide.edu.au> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7717 Archived-At: Hi all, I am just wondering where it was first stated (for both directions) that th= e category of coalgebras for a comonad on a Grothendieck topos E is again G= rothendieck if and only if the underlying endofunctor of E is accessible.=20 A modern argument might go as: the topos of coalgebras is Grothendieck if a= nd only if it is locally presentable if and only if the endofunctor is acce= ssible, the original probably just mentioned preservation of filtered colim= its. Many thanks, David Roberts= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]