From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1562 Path: news.gmane.org!not-for-mail From: Noson Yanofsky Newsgroups: gmane.science.mathematics.categories Subject: Preprint: Coherence, Homotopy and 2-Theories Date: Fri, 7 Jul 2000 17:19:13 -0400 Organization: Brooklyn College Message-ID: <01BFE837.793190C0.noson@sci.brooklyn.cuny.edu> Reply-To: "noson@sci.brooklyn.cuny.edu" NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241017925 31828 80.91.229.2 (29 Apr 2009 15:12:05 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:12:05 +0000 (UTC) To: "'categories@mta.ca'" Original-X-From: rrosebru@mta.ca Sat Jul 8 10:51:34 2000 -0300 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA24647 for categories-list; Sat, 8 Jul 2000 10:45:36 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: Microsoft Internet E-mail/MAPI - 8.0.0.4211 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 4 Original-Lines: 25 Xref: news.gmane.org gmane.science.mathematics.categories:1562 Archived-At: The following preprint is available on the xxx.lanl.gov archive: http://xxx.lanl.gov/abs/math.CT/0007033 Coherence, Homotopy and 2-Theories Authors: Noson S. Yanofsky Comments: 32 pages; XY-Pic Subj-class: Category Theory; Quantum Algebra MSC-class: 18D10; 18C10; 55U35 2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a Quillen model category structure on the category of 2-theories and 2-theory-morphisms where the weak equivalences are biequivalences of 2-theories. A biequivalence of 2-theories (Morita equivalence) induces and is induced by a biequivalence of 2-categories of algebras. This model category structure allows one to talk of the homotopy of 2-theories and discuss the universal properties of coherence. All the best, Noson