From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8271 Path: news.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: Re: cleavages and choice Date: Sat, 2 Aug 2014 12:58:18 +0200 Message-ID: References: <20140730150643.GC19613@mathematik.tu-darmstadt.de> <89048344-26F3-448F-8B41-9FF89AE1C892@wanadoo.fr> Reply-To: Marco Grandis NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v1085) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1407074466 3501 80.91.229.3 (3 Aug 2014 14:01:06 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 3 Aug 2014 14:01:06 +0000 (UTC) To: Eduardo Dubuc , categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sun Aug 03 16:00:55 2014 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 1XDwLF-0002HN-E1 for gsmc-categories@m.gmane.org; Sun, 03 Aug 2014 16:00:53 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:49907) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XDwKW-0004gR-C4; Sun, 03 Aug 2014 11:00:08 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XDwKV-0006ja-98 for categories-list@mlist.mta.ca; Sun, 03 Aug 2014 11:00:07 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8271 Archived-At: Dear Eduardo, I agree with many things in your message, but I think you are taking = your argument too far. Talking of pullbacks you say: > We precisely teach in category theory courses that you should not work = with any > particular choice between the choices. I agree that it is better to avoid such a choice when possible. Yet you = cannot define a bicategory of spans without assuming that such a choice = has been made; in the same way as you cannot define the (good) monoidal = structure of Ab without recurring to a choice of tensor products. Such a situation, we all know, generally arises in non-strict = bicategories (and monoidal categories, in particular). Unless you want to redefine bicategories replacing the composition of = arrows with an existence property. I still prefer working with a choice = (eg of pullbacks) to such a complicated structure. Best regards Marco= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]