From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7080 Path: news.gmane.org!not-for-mail From: David Leduc Newsgroups: gmane.science.mathematics.categories Subject: The category of categories as a 3-limit Date: Mon, 28 Nov 2011 12:04:31 +0000 Message-ID: Reply-To: David Leduc NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1322486850 17631 80.91.229.12 (28 Nov 2011 13:27:30 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 28 Nov 2011 13:27:30 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Mon Nov 28 14:27:23 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1RV1Ew-0003j7-QY for gsmc-categories@m.gmane.org; Mon, 28 Nov 2011 14:27:22 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:54306) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1RV1DS-0007vI-O6; Mon, 28 Nov 2011 09:25:50 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RV1DR-0006zr-0t for categories-list@mlist.mta.ca; Mon, 28 Nov 2011 09:25:49 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7080 Archived-At: Hi, In [1], Mike Shulman explains how one can define: * the category of magmas as an inserter in the 2-category of (large) categories, * the category of semigroups as an equifier, * and so on up to the category of rings. Can we go further? What is the 2-categorical limit to be used in order to define the category of small categories? But since small categories form a 2-category, maybe I should reformulate my question: What is the 3-categorical limit to be used in order to define the 2-category of small categories? While I am asking... What is the (n+2)-categorical limit to be used in order to define the (n+1)-category of n-categories? what is the omega-categorical limit to be used in order to define the omega-category of omega-categories? [1] http://mathoverflow.net/questions/9269/category-of-categories-as-a-foundation-of-mathematics [For admin and other information see: http://www.mta.ca/~cat-dist/ ]