From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5177 Path: news.gmane.org!not-for-mail From: Mark.Weber@pps.jussieu.fr Newsgroups: gmane.science.mathematics.categories Subject: 2 new papers on higher category theory Date: Mon, 28 Sep 2009 12:45:33 +0200 (CEST) Message-ID: Reply-To: Mark.Weber@pps.jussieu.fr 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: ger.gmane.org 1254141925 4876 80.91.229.12 (28 Sep 2009 12:45:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 28 Sep 2009 12:45:25 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Mon Sep 28 14:45:18 2009 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 4.50) id 1MsFbR-0002Ij-3c for gsmc-categories@m.gmane.org; Mon, 28 Sep 2009 14:45:17 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MsF0r-0002En-Jn for categories-list@mta.ca; Mon, 28 Sep 2009 09:07:29 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5177 Archived-At: Greetings. The following 2 papers Algebras of higher operads as enriched categories II (joint with Michael Batanin and Denis-Charles Cisinski) http://arxiv1.library.cornell.edu/abs/0909.4715 Abstract: One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [2] to adapt the machinery of globular operads [1] to this task. The resulting theory includes the Gray tensor product of 2-categories and the Crans tensor product [4] of Gray categories. Moreover much of the previous work on the globular approach to higher category theory is simplified by our new foundations, and we illustrate this by giving an expedited account of man= y aspects of Cheng's analysis [3] of Trimble's definition of weak n-category. By way of application we obtain an ``Ekmann-Hilton'' result for braided monoidal 2-categories, and give the construction of a tensor product of A-infinity algebras. Free Products of Higher Operad Algebras http://arxiv1.library.cornell.edu/abs/0909.4722 Abstract: In this paper we continue the developments of [2] and [5] by understanding the natural generalisations of Gray's little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable by an n-operad in the sense of Batanin [1], an analogous tensor product which forms a symmetric monoidal closed structure on the category of algebras of the operad. [1] M. Batanin. Monoidal globular categories as a natural environment for the theory of weak n-categories. Advances in Mathematics, 136:39=96103, 1998. [2] M. Batanin and M. Weber. Algebras of higher operads as enriched categories. Applied Categorical Structures, 38 pages, 2008. [3] E. Cheng. Comparing operadic theories of n-category, preprint, 2008. [4] S. Crans. A tensor product for Gray categories. Theory and applications of categories, 5:12=9669, 1999. [5] M. Batanin, D-C. Cisinski, and M. Weber. Algebras of higher operads a= s enriched categories II, preprint 57 pages, 2009. have recently been completed and are available at the above URL's or my new home-page http://sites.google.com/site/markwebersmaths/ Mark Weber [For admin and other information see: http://www.mta.ca/~cat-dist/ ]