From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9104 Path: news.gmane.org!.POSTED!not-for-mail From: =?ISO-8859-15?Q?Jir=ED_Ad=E1mek?= Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology Date: Wed, 8 Feb 2017 17:34:35 +0100 (CET) Message-ID: References: Reply-To: =?ISO-8859-15?Q?Jir=ED_Ad=E1mek?= NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; format=flowed; charset=US-ASCII X-Trace: blaine.gmane.org 1486651188 18120 195.159.176.226 (9 Feb 2017 14:39:48 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Thu, 9 Feb 2017 14:39:48 +0000 (UTC) To: categories net Original-X-From: majordomo@mlist.mta.ca Thu Feb 09 15:39:43 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 1cbpst-0004UK-IY for gsmc-categories@m.gmane.org; Thu, 09 Feb 2017 15:39:43 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:37137) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cbpps-0002x9-0h; Thu, 09 Feb 2017 10:36:36 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cbppM-0007vK-Ui for categories-list@mlist.mta.ca; Thu, 09 Feb 2017 10:36:04 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9104 Archived-At: 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/ ]