From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9278 Path: news.gmane.org!.POSTED!not-for-mail From: Mamuka Jibladze Newsgroups: gmane.science.mathematics.categories Subject: Do there exist nontrivial locally bounded geometric morphisms and/or locally (pre)sheaf =?UTF-8?Q?toposes=3F?= Date: Mon, 31 Jul 2017 12:07:18 +0400 Message-ID: Reply-To: Mamuka Jibladze NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit X-Trace: blaine.gmane.org 1501547426 27148 195.159.176.226 (1 Aug 2017 00:30:26 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 1 Aug 2017 00:30:26 +0000 (UTC) To: categories list Original-X-From: majordomo@mlist.mta.ca Tue Aug 01 02:30:21 2017 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 1dcL4i-0006Ru-Fd for gsmc-categories@m.gmane.org; Tue, 01 Aug 2017 02:30:16 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:39482) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dcL3o-0003XC-U6; Mon, 31 Jul 2017 21:29:20 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dcL3h-0002c8-KZ for categories-list@mlist.mta.ca; Mon, 31 Jul 2017 21:29:13 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9278 Archived-At: Recently I posted this question https://mathoverflow.net/q/277582/41291 to mathoverflow and now it occurred to me that most likely I can get a quick answer here. Are there geometric morphisms f: YY -> XX which are (1) locally but not globally bounded, or (2) locally but not globally presheaf, or (3) as in (2) and bounded? In more detail, I mean this: there must be an object X in XX with global support (X->1 epic) such that the pullback f/X: YY/f^*(X) -> XX/X is (1) bounded, while f is not bounded, or (2) equivalent over XX/X to the topos (XX/X)^{CC^op} of internal presheaves on some internal category CC of XX/X, while YY is not equivalent to any such over XX, or (3) same as (2) and in addition f bounded. Can any of these happen? Hoping, Mamuka [For admin and other information see: http://www.mta.ca/~cat-dist/ ]