From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9105 Path: news.gmane.org!.POSTED!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology Date: Thu, 9 Feb 2017 12:31:57 +0100 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: blaine.gmane.org 1486651192 18958 195.159.176.226 (9 Feb 2017 14:39:52 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Thu, 9 Feb 2017 14:39:52 +0000 (UTC) Cc: Categories To: Jean Benabou 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 1cbpst-0004Qs-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]:37158) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cbps2-00031f-Es; Thu, 09 Feb 2017 10:38:50 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cbprX-0007z8-6Q for categories-list@mlist.mta.ca; Thu, 09 Feb 2017 10:38:19 -0400 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9105 Archived-At: Dear Jean, in Remark 13.18 of their book on "Algebraic Theories" Adamek, Rosicky and Vitale suggest the following conditions 1) p faithful (what they call "concrete over X") 2) p-vertical isos are identities (what they call "amnestic")) 3) p is an isofibration (what they call "transportable") These seem to be reasonable conditions validated by most examples. Does this confirm with your intuition? Thomas > 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/ ]