From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7672 Path: news.gmane.org!not-for-mail From: Eduardo Pareja-Tobes Newsgroups: gmane.science.mathematics.categories Subject: Re: Name for a concept? Date: Fri, 26 Apr 2013 16:05:45 +0200 Message-ID: References: <838BC420-E6C8-49A1-8AD8-5A5C45E0D496@math.ksu.edu> Reply-To: Eduardo Pareja-Tobes NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1367067397 10099 80.91.229.3 (27 Apr 2013 12:56:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 27 Apr 2013 12:56:37 +0000 (UTC) Cc: David Yetter , categories To: "M. Bjerrum" Original-X-From: majordomo@mlist.mta.ca Sat Apr 27 14:56:41 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 1UW4gD-0006YM-Bi for gsmc-categories@m.gmane.org; Sat, 27 Apr 2013 14:56:41 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:38555) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1UW4f4-00014W-Jo; Sat, 27 Apr 2013 09:55:30 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1UW4f4-0007zr-11 for categories-list@mlist.mta.ca; Sat, 27 Apr 2013 09:55:30 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7672 Archived-At: =E2=80=8BHello Marie, Nice! =E2=80=8BSo, you think that none of protofiltered =E2=80=8Band pseudo-proto= filtered can be characterized as D-filtered for D a sound doctrine? waiting for your PhD thesis :) Eduardo Pareja-Tobes Math & CS freak *oh no sequences!* On Fri, Apr 26, 2013 at 3:03 PM, M. Bjerrum wrote: > Hello, > > I suppose that a span is a diagram of finitely many arrows of same domain > (or the op-situation). And the question concerns a name for categories wi= th > co-cones over all such diagrams. I don't have a very poetic name for this= . > At the moment I'm content with saying that such categories have V-cocones > (or V-cones) depending on directions. I've seen it being called the > "Amalgamation Property". > > But as to what concerns the connection with the question of mixed > interchange of limits in Set, one needs to be very careful: > > If for some doctrine D one defines D-filtered categories to be categories > J such that J-colimits commute with D-limits in Set, then this terminolog= y > will not do, since we then have. > > 1) If D is equalizers then D-filtered=3Dpseudofiltered. 2) If D is pullba= cks > then D-filtered=3Dpseudofiltered. 3) If D is pullbacks and terminal objec= ts, > then D-filtered=3Dfiltered (and not proto-pseudofilterd as one could hope= for) > > > So one need to distinguish between three things: > 1) having cocones over certain diagrams. > 2) the categories of cocones over certain diagrams are connected. 3) > commuting in Set with limits over certain diagrams. > > What has been called "sound doctrines", are the doctrines such that 2) an= d > 3) are equivalent. > > As a short answer to the open question: If J is a sifted + > proto-pseudofiltered category, i.e sifted and span-directed then J is > pseudofiltered and connected and thus filtered. (since pseudofiltered > categories are categories with filtered connected components) > > This kind of reflexions and more, with proofs, will soon be available via > my PhD thesis. > > Best wishes, > > Marie Bjerrum. > > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]