From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6262 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: The omega-functor omega-category Date: Thu, 30 Sep 2010 11:10:52 +0800 Message-ID: References: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: dough.gmane.org 1285898503 7634 80.91.229.12 (1 Oct 2010 02:01:43 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 1 Oct 2010 02:01:43 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Fri Oct 01 04:01:42 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1P1UwO-00078i-TJ for gsmc-categories@m.gmane.org; Fri, 01 Oct 2010 04:01:41 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:36458) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1P1Uvg-0005kp-Jn; Thu, 30 Sep 2010 23:00:56 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1P1Uvd-0001gi-Ag for categories-list@mlist.mta.ca; Thu, 30 Sep 2010 23:00:53 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6262 Archived-At: David Leduc wrote: >> I'm not sure what [_._] is supposed to mean - an internal >> hom functor? > This was supposed to be the "cartesian closed structure" of > StrictOmegaCat, but since some say it is not a structure I'm not sure > how to call it... Just call it the internal hom. The point is, you can just look at a category and say, yes or no, whether it's cartesian closed. So cartesian closedness is a "property" of a category - not a "structure" that you might equip a category with in more than one way. Nonetheless, you can consider properties as a special case of structures - namely, those structures for which you have at most one one choice. And if you do this you're free to speak of a cartesian closed "structure". Similarly, you can consider structures as a special case of "stuff". If you don't know the yoga of "properties, structure and stuff", you might enjoy this paper where Mike Shulman and I explain it: http://arxiv.org/PS_cache/math/pdf/0608/0608420v2.pdf#page=15 Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]