From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on inbox.vuxu.org X-Spam-Level: X-Spam-Status: No, score=-0.0 required=5.0 tests=RCVD_IN_MSPIKE_H2 autolearn=ham autolearn_force=no version=3.4.4 Received: (qmail 12566 invoked from network); 30 Jan 2023 20:14:37 -0000 Received: from smtp2.mta.ca (198.164.44.75) by inbox.vuxu.org with ESMTPUTF8; 30 Jan 2023 20:14:37 -0000 Received: from rr.mta.ca ([198.164.44.159]:40490) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1pMaXv-0001hw-1f; Mon, 30 Jan 2023 16:14:31 -0400 Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1pMaXE-000649-2N for categories-list@rr.mta.ca; Mon, 30 Jan 2023 16:13:48 -0400 Date: Mon, 30 Jan 2023 14:34:33 -0300 MIME-Version: 1.0 Subject: categories: Re: complete Galois groups Content-Language: en-US To: Clemens Berger , Pedro Resende Cc: Steven Vickers , categories list References: From: "Eduardo J. Dubuc" In-Reply-To: Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Precedence: bulk Reply-To: "Eduardo J. Dubuc" Message-Id: On 28/01/2023 07:48, Clemens Berger wrote: > How can we characterise ``intrinsically'' toposes that are of the > form BG for a complete Galois group G An observation that I do not know if of any help: What you want is how to characterize a pointed atomic (i.e. connected, locally connected, Boolean) topos p: G ---> Ens such that the morphism lAut(p) ---> Aut(p) is an isomorphism (where lAut is the localic group of automorphism). (recall that this localic group is explicitely constructed in my article "Localic Galois Theory") all the best Eduardo [For admin and other information see: http://www.mta.ca/~cat-dist/ ]