From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6886 Path: news.gmane.org!not-for-mail From: Rory Lucyshyn-Wright Newsgroups: gmane.science.mathematics.categories Subject: Totally distributive toposes Date: Mon, 12 Sep 2011 20:46:47 -0400 Message-ID: Reply-To: Rory Lucyshyn-Wright NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1315962905 16149 80.91.229.12 (14 Sep 2011 01:15:05 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 14 Sep 2011 01:15:05 +0000 (UTC) To: Original-X-From: majordomo@mlist.mta.ca Wed Sep 14 03:15:01 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1R3e45-00024m-FA for gsmc-categories@m.gmane.org; Wed, 14 Sep 2011 03:15:01 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:59375) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R3e2H-0006Ye-2X; Tue, 13 Sep 2011 22:13:09 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R3cwf-0007xD-TR for categories-list@mlist.mta.ca; Tue, 13 Sep 2011 21:03:17 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6886 Archived-At: My preprint "Totally distributive toposes" (http://arxiv.org/abs/1108.4032) has been updated to include an extended result, namely that the lex totally distributive categories with a small set of generators are exactly the injective Grothendieck toposes. Regards, Rory Lucyshyn-Wright Abstract: A locally small category E is totally distributive (as defined by Rosebrugh-Wood) if there exists a string of adjoint functors t -| c -| y, where y : E --> E^ is the Yoneda embedding. Saying that E is lex totally distributive if, moreover, the left adjoint t preserves finite limits, we show that the lex totally distributive categories with a small set of generators are exactly the injective Grothendieck toposes, studied by Johnstone and Joyal. We characterize the totally distributive categories with a small set of generators as exactly the essential subtoposes of presheaf toposes, studied by Kelly-Lawvere and Kennett-Riehl-Roy-Zaks. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]