From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8273 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: cleavages and choice Date: Sat, 02 Aug 2014 12:24:09 -0300 Message-ID: References: <20140730150643.GC19613@mathematik.tu-darmstadt.de> <89048344-26F3-448F-8B41-9FF89AE1C892@wanadoo.fr> <82157841-9DE2-4D99-8533-57AAB99CD236@dima.unige.it> Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1407074530 4103 80.91.229.3 (3 Aug 2014 14:02:10 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 3 Aug 2014 14:02:10 +0000 (UTC) Cc: categories@mta.ca To: Marco Grandis Original-X-From: majordomo@mlist.mta.ca Sun Aug 03 16:02:05 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 1XDwMN-0003le-IA for gsmc-categories@m.gmane.org; Sun, 03 Aug 2014 16:02:03 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:49919) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XDwM2-0004pf-V8; Sun, 03 Aug 2014 11:01:42 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XDwM1-0006lm-U6 for categories-list@mlist.mta.ca; Sun, 03 Aug 2014 11:01:41 -0300 In-Reply-To: <82157841-9DE2-4D99-8533-57AAB99CD236@dima.unige.it> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8273 Archived-At: Dear Marco, supposing you are right (which is probably the case, I have not examined closely the question of the monoidal structure of Ab or the bicategory of spans), this does not contradicts my points. I never said that choices should be banned, I said that they should not be used when not necessary, because of plenty of different reasons. best e.d. On 02/08/14 07:58, Marco Grandis wrote: > 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/ ]