From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7675 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology Date: Sat, 27 Apr 2013 15:08:57 +0200 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1367100501 16207 80.91.229.3 (27 Apr 2013 22:08:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 27 Apr 2013 22:08:21 +0000 (UTC) Cc: Categories To: Jean =?iso-8859-1?Q?B=E9nabou?= Original-X-From: majordomo@mlist.mta.ca Sun Apr 28 00:08:25 2013 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 1UWDI9-0002QG-Np for gsmc-categories@m.gmane.org; Sun, 28 Apr 2013 00:08:25 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:39733) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1UWDG5-0003lU-4o; Sat, 27 Apr 2013 19:06:17 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1UWDG6-0001vH-6O for categories-list@mlist.mta.ca; Sat, 27 Apr 2013 19:06:18 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7675 Archived-At: Dear Jean, > As many of you I presume, I have for ages, and very often, had to deal with categories which are both groupo?ds and posets, or again which are equivalent to a discrete category. Is there a well established name for them? What about "essentially discrete" like in "essentially small" or "essentially surjective". Generally, for any property P of categories I would say a category is "essentially P" if it is equivalent to a category with property P. So "essentially" is a kind of magic word transforming "evil" properties into "non-evil" ones. (I don't think one should always do this!) Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]