From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5811 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: terminology Date: Sat, 15 May 2010 12:05:02 -0400 Message-ID: References: Reply-To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1274024065 19169 80.91.229.12 (16 May 2010 15:34:25 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 16 May 2010 15:34:25 +0000 (UTC) To: "Michael Batanin" , "Toby Bartels" , Original-X-From: categories@mta.ca Sun May 16 17:34:22 2010 connect(): No such file or directory Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1ODfrA-0000d7-Tt for gsmc-categories@m.gmane.org; Sun, 16 May 2010 17:34:21 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1ODfKj-0006X8-UE for categories-list@mta.ca; Sun, 16 May 2010 12:00:50 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5811 Archived-At: Micheal Batanin wrote >If we follow the principle "foo =3D 1 foo" and want to agree >with historical low dimensional terminology we should call categories >2-sets. Set =3D 1 Set. So, categories =3D 2 Set. Nobody will do it I = guess. A few thoughts about terminology. Categories are tradidionally named according to the nature of their objects, not the nature of their morphisms.=20 We say "the category of sets" not "the category of functions".=20 This convention is not respected in the case where the category=20 has only one object: we call it a monoid, not because it is a=20 mono-object category (maybe we should) but because it has only one=20 binary operation in contrast with a ring.=20 Like monoids, operads are collections of abstract operations closed under composition. Classical operads have only one object, one color. But multi-colored operads are often called muti-categories, especially when they are big.=20 A set is a discrete homotopy type, a 0-type. This why I like to give the category of sets rank 0. I like to denote the quasi-category of n-types by U[n]. Best, Andr=E9 -------- Message d'origine-------- De: categories@mta.ca de la part de Michael Batanin Date: jeu. 13/05/2010 19:09 =C0: Toby Bartels Objet : categories: Re: bilax_monoidal_functors?=3D =20 >> Should we shift the >> numbers and call category a 3-category? > > No, but it seems to me that you are doing something very much like = this. Not at all. It may be was not a good example. A better example would be categories. If we follow the principle "foo =3D 1 foo" and want to agree with historical low dimensional terminology we should call categories 2-sets. Set =3D 1 Set. So, categories =3D 2 Set. Nobody will do it I = guess. There are many other examples like stack, gerbes and so on. I agree with Mike Shulman that this is a byproduct of categorification. But we can survive with it. ... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]