From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8279 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: cleavages and choice Date: Sun, 03 Aug 2014 17:41:59 -0300 Message-ID: References: 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 1407156632 458 80.91.229.3 (4 Aug 2014 12:50:32 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 4 Aug 2014 12:50:32 +0000 (UTC) Cc: categories@mta.ca To: Thomas Streicher Original-X-From: majordomo@mlist.mta.ca Mon Aug 04 14:50:25 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 1XEHiZ-0007J2-FW for gsmc-categories@m.gmane.org; Mon, 04 Aug 2014 14:50:23 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50082) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XEHiI-0007nK-2I; Mon, 04 Aug 2014 09:50:06 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XEHiG-0002rz-QU for categories-list@mlist.mta.ca; Mon, 04 Aug 2014 09:50:04 -0300 User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.9; rv:12.0) Gecko/20120428 Thunderbird/12.0.1 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8279 Archived-At: On 03/08/14 06:22, Thomas Streicher wrote: > One should not require all fibrations to be endowed with a cleavage. Rather > one should be open to accept some strong choice principles on the meta level > which allow one to assume the existence of cleavages whenever convenient. > But, definitely, one should give most definitions and constructions in a way > not referring to cleavages. I completely agree with this, it is my own feeling beautifully and synthetically expressed. I only add: "... most definitions and constructions AND proofs in a way ..." Also, that many times the use of cleavages may seem convenient, when in fact it is not. And I also put in the same bag the equivalences (which in general have only one direction. Then one should proceed using the fully-faithfulness and essentially surjectiveness whenever possible, and be free to assume the existence of quasi-inverses only if it is necessary. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]