From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9111 Path: news.gmane.org!.POSTED!not-for-mail From: "George Janelidze" Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology Date: Fri, 10 Feb 2017 03:42:15 +0200 Message-ID: References: Reply-To: "George Janelidze" NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=response Content-Transfer-Encoding: 8bit X-Trace: blaine.gmane.org 1486753152 6220 195.159.176.226 (10 Feb 2017 18:59:12 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Fri, 10 Feb 2017 18:59:12 +0000 (UTC) To: "categories net" , Original-X-From: majordomo@mlist.mta.ca Fri Feb 10 19:59:07 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1ccGPR-0001HD-S4 for gsmc-categories@m.gmane.org; Fri, 10 Feb 2017 19:59:06 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:39995) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1ccGLS-0003jK-9t; Fri, 10 Feb 2017 14:54:58 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ccGKw-0000my-Pu for categories-list@mlist.mta.ca; Fri, 10 Feb 2017 14:54:26 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9111 Archived-At: Dear Jean and Jiri, As we know there is no such notion accepted by everybody. I would probably vote for faithful + amnestic + iso-fibration. Best regards, George -------------------------------------------------- From: "Jir? Ad?mek" Sent: Wednesday, February 8, 2017 6:34 PM To: "categories net" Subject: categories: Re: Terminology > Dear Jean, > > The simplest answer is: faithful. But a better one (in view of > `everything up to isomorphism') is: faithful and amnestic. The latter > means that p reflects identity morphisms: an isomorphism in S is an > identity if its image by p is. See The Joy of Cats (free on the web). > > Best, Jiri > >> QUESTION >> Let p: S --> X be a functor. What conditions should satisfy p to be >> called a structure functor, i.e. such that every object s of S can be >> thought of as a structure on the object p(s). > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]