From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9106 Path: news.gmane.org!.POSTED!not-for-mail From: =?UTF-8?Q?Carsten_F=C3=BChrmann?= Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology Date: Wed, 08 Feb 2017 21:40:25 +0000 Message-ID: References: Reply-To: =?UTF-8?Q?Carsten_F=C3=BChrmann?= NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1486651193 19074 195.159.176.226 (9 Feb 2017 14:39:53 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Thu, 9 Feb 2017 14:39:53 +0000 (UTC) To: Jean Benabou , Categories Original-X-From: majordomo@mlist.mta.ca Thu Feb 09 15:39:48 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 1cbpsu-0004Wu-MU for gsmc-categories@m.gmane.org; Thu, 09 Feb 2017 15:39:44 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:37143) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cbpqp-0002yY-HC; Thu, 09 Feb 2017 10:37:35 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cbpqK-0007wL-CP for categories-list@mlist.mta.ca; Thu, 09 Feb 2017 10:37:04 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9106 Archived-At: Dear Jean, unless there is a technical meaning of "structure" I'm not aware of, the answer may be "Concrete categories" in the sense of Ad=C3=A1mek, Herrlich, = and Strecker: http://katmat.math.uni-bremen.de/acc/acc.pdf. A concrete category is just a faithful functor, but a remarkable amount of theory can be build on that notion. In particular, a classification of "algebra-like" and "space-like" structures is already possible at that level. On Wed, Feb 8, 2017 at 4:56 PM Jean Benabou wrote= : > Dear all, > > I'm sure the following question has been answered to. Could anyone > give me a precise answer and references to this answer. Many thanks. > > 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/ ]