From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8518 Path: news.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: Preprint: Limits in multiple categories Date: Thu, 26 Feb 2015 09:29:26 +0100 Message-ID: Reply-To: Marco Grandis NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1424957609 7760 80.91.229.3 (26 Feb 2015 13:33:29 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 26 Feb 2015 13:33:29 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Thu Feb 26 14:33:21 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1YQyZ0-0002wF-Ua for gsmc-categories@m.gmane.org; Thu, 26 Feb 2015 14:33:15 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:42776) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YQyXY-0005vz-S1; Thu, 26 Feb 2015 09:31:44 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YQyXY-0002vF-2Q for categories-list@mlist.mta.ca; Thu, 26 Feb 2015 09:31:44 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8518 Archived-At: There is now a second preprint in our series on multiple categories: M. Grandis - R. Par=E9 Limits in multiple categories (On weak and lax multiple categories, II) Pubbl. Mat. Univ. Genova, Preprint 605 (2015). http://www.dima.unige.it/~grandis/Mlc2.pdf Abstract. Continuing our first paper in this series, we study =20 multiple limits in infinite-dimensional multiple categories. The =20 general setting is chiral multiple categories - a weak, partially lax =20= form with directed interchanges. After defining multiple limits we prove that all of them can be =20 constructed from (multiple) products, equalisers and tabulators - all =20= of them assumed to be respected by faces and degeneracies. Tabulators =20= appear thus to be the basic higher limits, as was already the case =20 for double categories. Intercategories, a laxer form of multiple category already studied in =20= two previous papers, are also considered. In this more general =20 setting the basic multiple limits mentioned above can still be =20 defined, but their general theory is not developed here. The first paper of the series is: M. Grandis - R. Par=E9 An introduction to multiple categories (On weak and lax multiple =20 categories, I) Pubbl. Mat. Univ. Genova, Preprint 604 (2015). http://www.dima.unige.it/~grandis/Mlc1.pdf Marco Grandis and Bob Par=E9 . =09= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]