From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6708 Path: news.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: Preprint: From cubical to globular higher categories Date: Wed, 15 Jun 2011 14:00:18 +0200 Message-ID: Reply-To: Marco Grandis NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1308146269 7490 80.91.229.12 (15 Jun 2011 13:57:49 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 15 Jun 2011 13:57:49 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Jun 15 15:57:44 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QWqbI-0004dE-CB for gsmc-categories@m.gmane.org; Wed, 15 Jun 2011 15:57:44 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:49839) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QWqYZ-0008VH-4S; Wed, 15 Jun 2011 10:54:55 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QWqYY-0004Rb-Aj for categories-list@mlist.mta.ca; Wed, 15 Jun 2011 10:54:54 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6708 Archived-At: The following preprint is available M. Grandis - R. Pare From cubical to globular higher categories Dip. Mat. Univ. Genova, Preprint 594 (2011). http://www.dima.unige.it/~grandis/CGlb.pdf Abstract. We show that a strict symmetric (infinite-dimensional) cubical category A has an associated omega-category Glb(A), consisting of its 'globular cubes'. The procedure of globularisation generally destroys important features of A, like the existence of limits and colimits or the presence of symmetries. Then we examine the much more complex weak case, up to constructing the tricategory associated to a weak symmetric 3-cubical category. Best regards Marco Grandis [For admin and other information see: http://www.mta.ca/~cat-dist/ ]